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代数幾何学セミナー
過去の記録 ～05/18｜次回の予定｜今後の予定 05/19～
| 開催情報 | 金曜日 13:30～15:00 数理科学研究科棟(駒場) 118号室 |
|---|---|
| 担当者 | 權業 善範、河上 龍郎 、榎園 誠 |
今後の予定
2026年05月22日(金)
13:15-14:45 数理科学研究科棟(駒場) 117号室
Justin Sawon 氏 (University of North Carolina Chapel Hill)
Classification results for Lagrangian fibrations
Justin Sawon 氏 (University of North Carolina Chapel Hill)
Classification results for Lagrangian fibrations
[ 講演概要 ]
A Lagrangian fibration on a holomorphic symplectic manifold or variety is one whose general fibre is an abelian variety that is Lagrangian with respect to the symplectic form. Examples were constructed by Beauville/Mukai whose fibres are Jacobians of curves, and by Markushevich-Tikhomirov, Arbarella-Sacca-Ferretti, Matteini, S-Shen, and Brakkee-Camere-Grossi-Pertusi-Sacca-Viktorova whose fibres are Prym varieties of curves with involutions. In all of these examples the family of curves is a linear system on a K3 surface, suggesting the question: is this always the case? Markushevich answered this affirmatively in the genus two case: if the relative compactified Jacobian of a family of genus two curves is a Lagrangian fibration then the curves all lie on a K3 surface, and the Lagrangian fibration is a Beauville-Mukai system. In this talk I will describe our generalization of this result to higher genus, and also to relative Prym varieties of genus three covers with involutions (joint work with Xuqiang Qin).
A Lagrangian fibration on a holomorphic symplectic manifold or variety is one whose general fibre is an abelian variety that is Lagrangian with respect to the symplectic form. Examples were constructed by Beauville/Mukai whose fibres are Jacobians of curves, and by Markushevich-Tikhomirov, Arbarella-Sacca-Ferretti, Matteini, S-Shen, and Brakkee-Camere-Grossi-Pertusi-Sacca-Viktorova whose fibres are Prym varieties of curves with involutions. In all of these examples the family of curves is a linear system on a K3 surface, suggesting the question: is this always the case? Markushevich answered this affirmatively in the genus two case: if the relative compactified Jacobian of a family of genus two curves is a Lagrangian fibration then the curves all lie on a K3 surface, and the Lagrangian fibration is a Beauville-Mukai system. In this talk I will describe our generalization of this result to higher genus, and also to relative Prym varieties of genus three covers with involutions (joint work with Xuqiang Qin).
2026年05月29日(金)
13:15-14:45 数理科学研究科棟(駒場) 117号室
厚東 裕紀 氏 (Academia Sinica)
Towards a quantization of the Kirwan map via Fourier transform
厚東 裕紀 氏 (Academia Sinica)
Towards a quantization of the Kirwan map via Fourier transform
[ 講演概要 ]
Quantum cohomology ring is a deformation of the ordinary cohomology ring defined using counts of rational curves (genus zero Gromov-Witten invariants). In this talk, I will propose a Fourier transform for the quantum cohomology of smooth projective GIT quotients, viewed as a quantum analogue of the Kirwan map in ordinary cohomology. I will present several examples where this Fourier transform can be constructed and discuss some applications. This talk is based on ongoing work.
Quantum cohomology ring is a deformation of the ordinary cohomology ring defined using counts of rational curves (genus zero Gromov-Witten invariants). In this talk, I will propose a Fourier transform for the quantum cohomology of smooth projective GIT quotients, viewed as a quantum analogue of the Kirwan map in ordinary cohomology. I will present several examples where this Fourier transform can be constructed and discuss some applications. This talk is based on ongoing work.
2026年06月05日(金)
14:00-15:00 数理科学研究科棟(駒場) 大講義室（NISSAY Lecture Hall）号室
Young-Hoon Kiem 氏 (Korea Institute for Advanced Study)
Cohomology of moduli spaces of curves
Young-Hoon Kiem 氏 (Korea Institute for Advanced Study)
Cohomology of moduli spaces of curves
[ 講演概要 ]
Moduli spaces of stable pointed curves have been much studied but still we know surprisingly little about their cohomology. In this talk, I will discuss some recent progresses based on techniques from combinatorics and probability theory as well as the algebraic geometry of wall crossings in the stack of maps.
Moduli spaces of stable pointed curves have been much studied but still we know surprisingly little about their cohomology. In this talk, I will discuss some recent progresses based on techniques from combinatorics and probability theory as well as the algebraic geometry of wall crossings in the stack of maps.
