Research activity information

• Length of triangulated categories
  Yuki Hirano; Martin Kalck; Genki Ouchi
  Advances in Mathematics, 483, 110660, 110660, Elsevier BV, Dec. 2025, [Peer-reviewed]
  Scientific journal
• Thurston compactifications of spaces of stability conditions on curves
  Kohei Kikuta; Naoki Koseki; Genki Ouchi
  Transactions of the American Mathematical Society, American Mathematical Society (AMS), 13 Feb. 2024, [Peer-reviewed]
  Scientific journal,

  In this paper, we construct a compactification of the space of Bridgeland stability conditions on a smooth projective curve, as an analogue of Thurston compactifications in Teichmüller theory.

  In the case of elliptic curves, we compare our results with the classical one of the torus via homological mirror symmetry and give the Nielsen–Thurston classification of autoequivalences using the compactification.

  Furthermore, we observe an interesting phenomenon in the case of the projective line.

• Perverse schobers and Orlov equivalences
  Naoki Koseki; Genki Ouchi
  European Journal of Mathematics, 9, 2, Springer Science and Business Media LLC, 28 Apr. 2023, [Peer-reviewed]
  Scientific journal, Abstract
  
  A perverse schober is a categorification of a perverse sheaf proposed by Kapranov–Schechtman. In this paper, we construct examples of perverse schobers on the Riemann sphere, which categorify the intersection complexes of natural local systems arising from the mirror symmetry for Calabi–Yau hypersurfaces. The Orlov equivalence plays a key role for the construction.
• Derived factorization categories of non‐Thom–Sebastiani‐type sums of potentials
  Yuki Hirano; Genki Ouchi
  Proceedings of the London Mathematical Society, 126, 1, 1, 75, Wiley, 22 Sep. 2022, [Peer-reviewed]
  Scientific journal
• Prime thick subcategories on elliptic curves
  Yuki Hirano; Genki Ouchi
  Pacific Journal of Mathematics, 318, 1, 69, 88, Mathematical Sciences Publishers, 01 Aug. 2022, [Peer-reviewed]
  Scientific journal
• Hochschild Entropy and Categorical Entropy
  Kohei Kikuta; Genki Ouchi
  Arnold Mathematical Journal, 9, 2, 223, 244, Springer Science and Business Media LLC, 18 Jul. 2022, [Peer-reviewed]
  Scientific journal
• Categorical polynomial entropy
  Yu-Wei Fan; Lie Fu; Genki Ouchi
  Advances in Mathematics, 383, 107655, 107655, Elsevier BV, Jun. 2021, [Peer-reviewed]
  Scientific journal
• Serre dimension and stability conditions
  Kohei Kikuta; Genki Ouchi; Atsushi Takahashi
  Mathematische Zeitschrift, 299, 1-2, 997, 1013, Springer Science and Business Media LLC, 04 Mar. 2021, [Peer-reviewed]
  Scientific journal
• Automorphism groups of cubic fourfolds and K3 categories
  Genki Ouchi
  Algebraic Geometry, 171, 195, Foundation Compositio Mathematica, 01 Mar. 2021, [Peer-reviewed]
  Scientific journal
• Hilbert schemes of two points on K3 surfaces and certain rational cubic fourfolds
  Genki Ouchi
  Communications in Algebra, 49, 3, 1173, 1179, Informa UK Limited, 05 Nov. 2020, [Peer-reviewed]
  Scientific journal
• On entropy of spherical twists
  Genki Ouchi
  Proceedings of the American Mathematical Society, 148, 3, 1003, 1014, American Mathematical Society (AMS), 18 Oct. 2019, [Peer-reviewed]
  Scientific journal,

  In this paper, we compute categorical entropy of spherical twists. In particular, we prove that the Gromov–Yomdin-type conjecture holds for spherical twists. Moreover, we construct counterexamples of Gromov–Yomdin type conjecture for K3 surfaces modifying Fan’s construction for even higher-dimensional Calabi–Yau manifolds.

  The appendix, by Arend Bayer, shows the nonemptiness of complements of a number of spherical objects in the derived categories of K3 surfaces.

• Automorphisms of positive entropy on some hyperKähler manifolds via derived automorphisms of K3 surfaces
  Genki Ouchi
  Advances in Mathematics, 335, 1, 26, Elsevier BV, Sep. 2018, [Peer-reviewed]
  Scientific journal
• Lagrangian embeddings of cubic fourfolds containing a plane
  Genki Ouchi
  Compositio Mathematica, 153, 5, 947, 972, Wiley, 23 Mar. 2017, [Peer-reviewed]
  Scientific journal, We prove that a very general smooth cubic fourfold containing a plane can be embedded into an irreducible holomorphic symplectic eightfold as a Lagrangian submanifold. We construct the desired irreducible holomorphic symplectic eightfold as a moduli space of Bridgeland stable objects in the derived category of the twisted K3 surface corresponding to the cubic fourfold containing a plane.

• Calabi-Yau多様体の自己同型と不変量の研究
  科学研究費助成事業
  Apr. 2019 - Mar. 2025
  大内 元気
  今年度は、主にperverse schoberや三角圏のスペクトラムについて研究を行った。
  1. perverse schoberは、KapranovとSchechtmanが導入したperverse sheafの圏論化であり、三角圏の自己同値の研究に新しい視点をもたらすものである。perverse schoberの例を構成することは、自己同値をspherical functorのtwistとして表示することとおおよそ対応している。今年度は、小関直紀氏との共同研究でCalabi-Yau超曲面の導来圏について、すでに知られている圏の局所系を延長するようなperverse schoberをいくつか構成した。
  
  
  2. Balmerはテンソル三角圏に対して、スペクトラムという環付き空間を構成し、代数幾何学の文脈ではテンソル三角圏を用いて、スキームを復元できることを示した。松井氏は、三角圏に対してスペクトラムという位相空間を導入し、その基本的性質やBalmerのスペクトラムとの関係を調べた。連接層の導来圏に対して、松井氏のスペクトラムはすべてのフーリエ向井パートナーを含み、興味深い対象である。今年度は、平野雄貴氏との共同研究で楕円曲線の導来圏のスペクトラムを完全に決定した。また、（反）標準因子が豊富な滑らかな射影的な代数多様体Xの導来圏のスペクトラムの中でXをSerre関手を用いて特徴付けた。さらに、フロップによる導来同値、モジュライ空間の普遍族を用いて得られる導来同値について考察することで、フーリエ向井パートナーが松井氏のスペクトラムの中で交わることも交わらないこともあることがわかった。
  日本学術振興会, 若手研究, 19K14520