Researcher Database

JINZENJI Masao
Faculty of Science Mathematics Mathematics
Associate Professor

Researcher Profile and Settings

Affiliation

  • Faculty of Science Mathematics Mathematics

Job Title

    Associate Professor

Research Interests

  • Topological Field Theory   

Research Areas

  • Mathematics / Geometry
  • Physics / Mathematical physics/Fundamental condensed matter physics
  • Mathematics / Algebra
  • Physics / Mathematical physics/Fundamental condensed matter physics
  • Mathematics / Geometry

Academic & Professional Experience

  • 2007    - Associate Professor

Research Activities

Published Papers

Books etc

  • Classical Mirror Symmetry
    JINZENJI Masao (Professional, Graduate Students)
    Springer Singapore 2018/04 978-981-13-0055-4 148 Single Work

MISC

  • Masao Jinzenji  2017/12   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    In this paper, we outline geometrical proof of the generalized mirror transformation of genus 0 Gromov-Witten invariants of degree k hypersurface in CP^{N-1}.
  • Masao Jinzenji, Masahide Shimizu  Communications in Number Theory and Physics, Volume 7, Number 3, 411-468, 2013  2013/05   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    In this paper, we propose a geometrical approach to mirror computation of genus 0 Gromov-Witten invariants of CP^2. We use multi-point virtual structure constants, which are defined as intersection numbers of a compact moduli space of quasi maps from CP^1 to CP^2 with 2+n marked points. We conjecture that some generating functions of them produce mirror map and the others are translated into generating functions of Gromov-Witten invariants via the mirror map. We generalize this formalism to open string case. In this case, we have to introduce infinite number of deformation parameters to obtain results that agree with some known results of open Gromov-Witten invariants of CP^2. We also apply multi-point virtual structure constants to compute closed and open Gromov-Witten invariants of a non-nef hypersurface in projective space. This application simplifies the computational process of generalized mirror transformation.
  • Masao Jinzenji, Masahide Shimizu  International Journal of Geometric Methods in Modern Physics, Vol.11, No.1 (2014) 1450005  2011/08   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    In this paper, we generalize Walcher's computation of the open Gromov-Witten invariants of the quintic hypersurface to Fano and Calabi-Yau projective hypersurfaces. Our main tool is the open virtual structure constants. We also propose the generalized mirror transformation for the open Gromov-Witten invariants, some parts of which are proven explicitly. We also discuss possible modification of the multiple covering formula for the case of higher dimensional Calabi-Yau manifolds. The generalized disk invariants for some Calabi-Yau and Fano manifolds are shown and they are certainly integers after re-summation by the modified multiple covering formula. This paper also contains the direct integration method of the period integrals for higher dimensional Calabi-Yau hypersurfaces in the appendix.
  • Masao Jinzenji  Communications in Mathematical Physics, 323, 747--811 (2013)  2010/06   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    In this paper, we extend our geometrical derivation of expansion coefficients of mirror maps by localization computation to the case of toric manifolds with two K\"ahler forms. Especially, we take Hirzebruch surfaces F_{0}, F_{3} and Calabi-Yau hypersurface in weighted projective space P(1,1,2,2,2) as examples. We expect that our results can be easily generalized to arbitrary toric manifold.
  • Masao Jinzenji  Journal of Geometry and Physics, Vol. 61, Issue 8, (2011) 1564-1573  61-  (8)  1564  -1573  2009/02   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    In this paper, we directly derive generalized mirror transformation of projective hypersurfaces up to degree 3 genus 0 Gromov-Witten invariants by comparing Kontsevich localization formula with residue integral representation of the virtual structure constants. We can easily generalize our method for rational curves of arbitrary degree except for combinatorial complexities.
  • Brian Forbes, Masao Jinzenji  Adv.Theor.Math.Phys.11:175-197,2007  2006/09   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    We continue our study of equivariant local mirror symmetry of curves, i.e. mirror symmetry for X_k=O(k)+O(-2-k) over P^1 with torus action (lambda_1,lambda_2) on the bundle. For the antidiagonal action lambda_1=-lambda_2, we find closed formulas for the mirror map and a rational B model Yukawa coupling for all k. Moreover, we give a simple closed form for the B model genus 1 Gromov-Witten potential. For the diagonal action lambda_1=lambda_2, we argue that the mirror symmetry computation is equivalent to that of the projective bundle P(O+O(k)+O(-2-k)) over P^1. Finally, we outline the computation of equivariant Gromov-Witten invariants for A_n singularities and toric tree examples via mirror symmetry.
  • Brian Forbes, Masao Jinzenji  Int.J.Mod.Phys.A22:2327-2360,2007  2006/03   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    We develop techniques for computing the equivariant local mirror symmetry of curves, i.e. mirror symmetry for O(k)+O(-2-k) over P^1 for k greater than 0. We also describe related methods for dealing with mirror symmetry of non-nef toric varieties. The basic tools are equivariant I functions and their Birkhoff factorization.
  • Masao Jinzenji, Toru Sasaki  JHEP 0209 (2002) 002  2002/03   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    We propose a recipe for determination of the partition function of ${\cal N}=4$ $ADE$ gauge theory on $K3$ by generalizing our previous results of the SU(N) case. The resulting partition function satisfies Montonen-Olive duality for $ADE $ gauge group.
  • Masao Jinzenji, Toru Sasaki  JHEP 0112:002,2001  2001/09   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    We derive the partition function of {\cal N}=4 supersymmetric Yang-Mills theory on orbifold-T^4/{\bf Z}_2 for gauge group SU(N). We generalize the method of our previous work for the SU(2) case to the SU(N) case. The resulting partition function is represented as the sum of the product of G\"ottche formula of singular quotient space $T^4/{\bf Z}_2 $ and of blow-up formulas including A_{N-1} theta series with level N.
  • Masao Jinzenji  Int.J.Math. 13 (2002) 445-478  2001/09   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    In this paper, we discuss some applications of Givental's differential equations to enumerative problems on rational curves in projective hypersurfaces. Using this method, we prove some of the conjectures on the structure constants of quantum cohomology of projective hypersurfaces, proposed in our previous article. Moreover, we clarify the correspondence between the virtual structure constants and Givental's differential equations when the projective hypersurface is Calabi-Yau or general type.
  • Masao Jinzenji  Mod.Phys.Lett. A15 (2000) 629-650  15-  629  -650  2000/02   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    In this paper, we propose another characterization of the generalized mirror transformation on the quantum cohomology rings of general type projective hypersurfaces. This characterics is useful for explicit determination of the form of the generalized mirror transformation. As applications, we rederive the generalized mirror transformation up to $d=3$ rational Gromov-Witten invariants obtained in our previous article, and determine explicitly the the generalized mirror transformation for the $d=4, 5$ rational Gromov-Witten invariants in the case when the first Chern class of the hypersurface equals $-H$ (i.e., $k-N=1$).
  • Masao Jinzenji, Toru Sasaki  Mod.Phys.Lett. A16 (2001) 411-428  2000/12   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    We derive the partition function of N=4 supersymmetric Yang-Mills theory on orbifold-$T^4/{\bf Z}_2$. In classical geometry, K3 surface is constructed from the orbifold-$T^4/{\bf Z}_2$. Along the same way as the orbifold construction, we construct the partition function of K3 surface from orbifold-$T^4/{\bf Z}_2$. The partition function is given by the product of the contribution of the untwisted sector of $T^4/{\bf Z}_2$, and that of the twisted sector of $T^4/{\bf Z}_2$ i.e., ${\cal O}(-2)$ curve blow-up formula.
  • Brian Forbes, Masao Jinzenji  JHEP0603:061,2006  2005/11   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    In this paper, we first derive an intrinsic definition of classical triple intersection numbers of K_S, where S is a complex toric surface, and use this to compute the extended Picard-Fuchs system of K_S of our previous paper, without making use of the instanton expansion. We then extend this formalism to local fourfolds K_X, where X is a complex 3-fold. As a result, we are able to fix the prepotential of local Calabi-Yau threefolds K_S up to polynomial terms of degree 2. We then outline methods of extending the procedure to non canonical bundle cases.
  • Masao Jinzenji  Letters in Mathematical Physics, Vol.86, No.2-3, 99-114 (2008)  86-  (2-3)  99  -114  2007/12   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    In this paper, we derive the virtual structure constants used in mirror computation of degree k hypersurface in CP^{N-1}, by using localization computation applied to moduli space of polynomial maps from CP^{1} to CP^{N-1} with two marked points. We also apply this technique to non-nef local geometry O(1)+O(-3)->CP^{1} and realize mirror computation without using Birkhoff factorization.
  • Masao Jinzenji  Int.J.Mod.Phys. A20 (2005) 2131-2156  20-  (10)  2131  -2156  2003/10   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    In this paper, we explicitly derive the generalized mirror transformation of quantum cohomology of general type projective hypersurfaces, proposed in our previous article, as an effect of coordinate change of the virtual Gauss-Manin system.
  • Tohru Eguchi, Masao Jinzenji  JHEP 0002 (2000) 028  1999/11   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    We discuss a possible generalization of the Calabi-Yau/Landau-Ginzburg correspondence to a more general class of manifolds. Specifically we consider the Fermat type hypersurfaces $M_N^k$: $\sum_{i=1}^N X_i^k =0$ in ${\bf CP}^{N-1}$ for various values of k and N. When k2. We assume that this massless sector is described by a Landau-Ginzburg (LG) theory of central charge $c=3N(1-2/k)$ with N chiral fields with U(1) charge $1/k$. We compute the topological invariants (elliptic genera) using LG theory and massive vacua and compare them with the geometrical data. We find that the results agree if and only if k=even and N=even. These are the cases when the hypersurfaces have a spin structure. Thus we find an evidence for the geometry/LG correspondence in the case of spin manifolds.
  • M. Jinzenji  Mod.Phys.Lett. A15 (2000) 101-120  15-  101  -120  1999/10   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    In this paper, we propose the formulas that compute all the rational structural constants of the quantum K\"ahler sub-ring of Fano hypersurfaces.
  • Brian Forbes, Masao Jinzenji  J.Math.Phys. 46 (2005) 082302  46-  (8)  1  -82302  2005/03   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    We propose an extended set of differential operators for local mirror symmetry. If $X$ is Calabi-Yau such that $\dim H_4(X,\Z)=0$, then we show that our operators fully describe mirror symmetry. In the process, a conjecture for intersection theory for such $X$ is uncovered. We also find new operators on several examples of type $X=K_S$ through similar techniques. In addition, open string PF systems are considered.
  • Jinzenji Masao  Soryushiron Kenkyu  97-  (4)  D119  -D127  1998/07   [Not refereed] [Not invited]  
    In this paper, we review recent discovery of connection between Virasoro algebra and topological sigma model coupled to topological gravity.
  • Brian Forbes, Masao Jinzenji  Commun.Num.Theor.Phys.1,2007  729  2007/09   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    We solve the problem of equivariant mirror symmetry for O(-3)->P^2 for the (three) cases of one independent equivariant parameter. This gives a decomposition of mirror symmetry for local P^2 into that of three subspaces, each of which may be considered independently. Finally, we give a new interpretation of mirror symmetry for O(k)+O(-2-k)->P^1.
  • M. Jinzenji  Int.J.Mod.Phys.A15:1557-1596,2000  1998/11   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    In this paper, we study the structure of the quantum cohomology ring of a projective hypersurface with non-positive 1st Chern class. We prove a theorem which suggests that the mirror transformation of the quantum cohomology of a projective Calabi-Yau hypersurface has a close relation with the ring of symmetric functions, or with Schur polynomials. With this result in mind, we propose a generalized mirror transformation on the quantum cohomology of a hypersurface with negative first Chern class and construct an explicit prediction formula for three point Gromov-Witten invariants up to cubic rational curves. We also construct a projective space resolution of the moduli space of polynomial maps, which is in a good correspondence with the terms that appear in the generalized mirror transformation.
  • Tohru Eguchi, Masao Jinzenji, Chuan-Sheng Xiong  Nucl.Phys. B510 (1998) 608-622  1997/09   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    In our previous article we have proposed that the Virasoro algebra controls the quantum cohomology of Fano varieties at all genera. In this paper we construct a free field description of Virasoro operators and quantum cohomology. We shall show that to each even (odd) homology class of a K\"{a}hler manifold we have a free bosonic (fermionic) field and Virasoro operators are given by a simple bilinear form of these fields. We shall show that the Virasoro condition correctly reproduces the Gromov-Witten invariants also in the case of manifolds with non-vanishing non-analytic classes ($h^{p,q}\not=0,p\not=q$) and suggest that the Virasoro condition holds universally for all compact smooth K\"{a}hler manifolds.
  • A. Collino, M. Jinzenji  Commun.Math.Phys. 206 (1999) 157-183  1996/11   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    We give an explicit procedure which computes for degree $d \leq 3$ the correlation functions of topological sigma model (A-model) on a projective Fano hypersurface $X$ as homogeneous polynomials of degree $d$ in the correlation functions of degree 1 (number of lines). We extend this formalism to the case of Calabi-Yau hypersurfaces and explain how the polynomial property is preserved. Our key tool is the construction of universal recursive formulas which express the structural constants of the quantum cohomology ring of $X$ as weighted homogeneous polynomial functions in the constants of the Fano hypersurface with the same degree and dimension one more. We propose some conjectures about the existence and the form of the recursive formulas for the structural constants of rational curves of arbitrary degree. Our recursive formulas should yield the coefficients of the hypergeometric series used in the mirror calculation. Assuming the validity of the conjectures we find the recursive laws for rational curves of degree 4 and 5.
  • Masao Jinzenji  J.Math.Phys. 38 (1997) 6613-6638  38-  (12)  6613  -6638  1995/11   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    Using the torus action method, we construct one variable polynomial representation of quantum cohomology ring for degree $k$ hypersurface in $CP^{N-1}$ . The results interpolate the well-known result of $CP^{N-2}$ model and the one of Calabi-Yau hypersuface in $CP^{N-1}$. We find in $k\leq N-2$ case, principal relation of this ring have very simple form compatible with toric compactification of moduli space of holomorphic maps from $CP^{1}$ to $CP^{N-1}$.
  • Masao Jinzenji  Int.J.Mod.Phys. A12 (1997) 5775-5802  12-  (32)  5775  -5802  1995/05   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    We calculate correlation functions of topological sigma model (A-model) on Calabi-Yau hypersurfaces in $CP^{N-1}$ using torus action method. We also obtain path-integral represention of free energy of the theory coupled to gravity.
  • Masao Jinzenji, Masaru Nagura  Int.J.Mod.Phys. A11 (1996) 1217-1252  1994/09   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    We consider an (N-2)-dimensional Calabi-Yau manifold which is defined as the zero locus of the polynomial of degree N (of Fermat type) in CP^{N-1} and its mirror manifold. We introduce the (N-2)-point correlation function (generalized Yukawa coupling) and evaluate it both by solving the Picard-Fuchs equation for period integrals in the mirror manifold and also by explicitly calculating the contribution of holomorphic maps of degree 1 to the Yukawa coupling in the Calabi-Yau manifold using the method of Algebraic geometry...
  • Masao Jinzenji, Yi Sun  Int.J.Mod.Phys. A11 (1996) 171-202  11-  (1)  171  -202  1994/12   [Not refereed] [Not invited]  Institution technical report and pre-print, etc.  
    Using the associativity relations of the topological Sigma Models with target spaces, $CP^3, CP^4$ and $Gr(2,4)$ , we derive recursion relations of their correlation and evaluate them up to certain order in the expansion over the instantons. The expansion coeffieients are regarded as the number of rational curves in $CP^3, CP^4$ and $Gr(2,4)$ which intersect various types of submanifolds corresponding to the choice of BRST invariant operators in the correlation functions.

Research Grants & Projects

  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(基盤研究(C))
    Date (from‐to) : 2010 -2012 
    Author : Masao JINZENJI
     
    北海道大学We reconstructed the mirror map, which is used in the mirror computation of Gromov-Witten invariants, as a generating function of intersection numbers of the moduli space of quasi maps. With this result, we reinterpreted the mirror computation of Gromov-Witten invariants as a way of computing Gromov-Witten invariants by using the difference of compactification of the moduli space of holomorphic maps. We also used this reconstruction to generalize the mirror computation of open Gromov-Witten invariants to wide class of complex manifolds.

Educational Activities

Teaching Experience

  • 現代数学概説
    開講年度 : 2017
    課程区分 : 修士課程
    開講学部 : 理学院
  • Geometry
    開講年度 : 2017
    課程区分 : 修士課程
    開講学部 : 理学院
    キーワード : はめ込みとしずめ込み 横断性 交差理論 ポアンカレ-ホップの定理
  • Overview of Modern Mathematics
    開講年度 : 2017
    課程区分 : 修士課程
    開講学部 : 理学院
    キーワード : 【有限鏡映群について】 鏡映群, 折り返し, 平面分割, 空間分割 【有理曲線の数え上げとミラー対称性】 有理曲線、グロモフ‐ウィッテン不変量、ミラー対称性
  • Inter-Graduate School Classes(General Subject):Natural and Applied Sciences
    開講年度 : 2017
    課程区分 : 修士課程
    開講学部 : 大学院共通科目
    キーワード : 【有限鏡映群について】 鏡映群, 折り返し, 平面分割, 空間分割 【有理曲線の数え上げとミラー対称性】 有理曲線、グロモフ‐ウィッテン不変量、ミラー対称性
  • Advanced Geometry
    開講年度 : 2017
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : はめ込みとしずめ込み 横断性 交差理論 ポアンカレ-ホップの定理
  • Calculus I
    開講年度 : 2017
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : 数列, 収束, 関数, 極限, 微分, 偏微分, テイラ-の定理
  • Calculus II
    開講年度 : 2017
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : 原始関数, 積分, 重積分, リ-マン和, 変数変換
  • Exercises on Basic Mathematics C
    開講年度 : 2017
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : 実数、数列、収束、連続、微分、積分


Copyright c MEDIA FUSION Co.,Ltd. All rights reserved.