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代数幾何学セミナー
過去の記録 ～01/02｜次回の予定｜今後の予定 01/03～
| 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01月07日(水)
10:30-12:00 数理科学研究科棟(駒場) 122号室
いつもと曜日・時間が異なります。
Jun-Muk Hwang 氏 (IBS Center for Complex Geometry)
Fundamental forms and infinitesimal symmetries of projective varieties
いつもと曜日・時間が異なります。
Jun-Muk Hwang 氏 (IBS Center for Complex Geometry)
Fundamental forms and infinitesimal symmetries of projective varieties
[ 講演概要 ]
We give a bound on the dimension of the linear automorphism group of a projective variety $Z \subset P^n$ in terms of its fundamental forms at a general point. Moreover, we show that the bound is achieved precisely when $Z \subset P^n$ is projectively equivalent to an Euler-symmetric variety. As a by-product, we determine the Lie algebra of infinitesimal automorphisms of an Euler-symmetric variety and also obtain a rigidity result on the specialization of an Euler-symmetric variety preserving the isomorphism type of the fundamental forms. This is a joint work with Qifeng Li.
We give a bound on the dimension of the linear automorphism group of a projective variety $Z \subset P^n$ in terms of its fundamental forms at a general point. Moreover, we show that the bound is achieved precisely when $Z \subset P^n$ is projectively equivalent to an Euler-symmetric variety. As a by-product, we determine the Lie algebra of infinitesimal automorphisms of an Euler-symmetric variety and also obtain a rigidity result on the specialization of an Euler-symmetric variety preserving the isomorphism type of the fundamental forms. This is a joint work with Qifeng Li.
2026年01月14日(水)
13:30-15:00 数理科学研究科棟(駒場) 122号室
いつもと曜日が異なります．いつもと部屋が異なります．
Radu Laza 氏 (Stony Brook University)
TBA
いつもと曜日が異なります．いつもと部屋が異なります．
Radu Laza 氏 (Stony Brook University)
TBA
[ 講演概要 ]
TBA
TBA
2026年01月16日(金)
13:30-15:00 数理科学研究科棟(駒場) 118号室
朝永龍 氏 (東京大学)
On d-tilting bundles on d-folds
朝永龍 氏 (東京大学)
On d-tilting bundles on d-folds
[ 講演概要 ]
A d-tilting bundle is a tilting bundle whose endomorphism algebra has global dimension at most d. On d-dimensional smooth projective varieties, d-tilting bundles generalize geometric helices and play an important role in connections with tilting bundles on the total space of the canonical bundle (Calabi-Yau completion), non-commutative crepant resolutions and higher Auslander-Reiten theory.
In this talk, we prove the following results. First, if a d-dimensional smooth projective variety has a d-tilting bundle, then it is weak Fano. Second, every weak del Pezzo surface has a 2-tilting bundle. As an application, we show that every singular del Pezzo cone admits a non-commutative crepant resolution.
If time permits, we will also present a classification of d-tilting bundles consisting of line bundles on d-dimensional smooth toric Fano stacks of Picard number one or two.
A d-tilting bundle is a tilting bundle whose endomorphism algebra has global dimension at most d. On d-dimensional smooth projective varieties, d-tilting bundles generalize geometric helices and play an important role in connections with tilting bundles on the total space of the canonical bundle (Calabi-Yau completion), non-commutative crepant resolutions and higher Auslander-Reiten theory.
In this talk, we prove the following results. First, if a d-dimensional smooth projective variety has a d-tilting bundle, then it is weak Fano. Second, every weak del Pezzo surface has a 2-tilting bundle. As an application, we show that every singular del Pezzo cone admits a non-commutative crepant resolution.
If time permits, we will also present a classification of d-tilting bundles consisting of line bundles on d-dimensional smooth toric Fano stacks of Picard number one or two.
