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過去の記録 ～01/15｜本日 01/16 | 今後の予定 01/17～
2026年01月16日(金)
代数幾何学セミナー
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.
