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代数幾何学セミナー
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| 開催情報 | 金曜日 13:30～15:00 数理科学研究科棟(駒場) ハイブリッド開催/117号室 |
|---|---|
| 担当者 | 權業 善範、中村 勇哉、田中 公 |
2016年07月05日(火)
15:30-17:00 数理科学研究科棟(駒場) 122号室
Dulip Piyaratne 氏 (IPMU)
Generalized Bogomolov-Gieseker type inequality for Fano 3-folds (English)
Dulip Piyaratne 氏 (IPMU)
Generalized Bogomolov-Gieseker type inequality for Fano 3-folds (English)
[ 講演概要 ]
Construction of Bridgeland stability conditions on a given smooth projective 3-fold is an important problem. A conjectural construction for any 3-fold was introduced by Bayer, Macri and Toda, and the problem is reduced to proving so-called Bogomolov-Gieseker type inequality holds for certain stable objects in the derived category. It has been shown to hold for Fano 3-folds of Picard rank one due to the works of Macri, Schmidt and Li. However, Schmidt gave a counter-example for a Fano 3-fold of higher Picard rank. In this talk, I will explain how to modify the original conjectural inequality for general Fano 3-folds and why it holds.
Construction of Bridgeland stability conditions on a given smooth projective 3-fold is an important problem. A conjectural construction for any 3-fold was introduced by Bayer, Macri and Toda, and the problem is reduced to proving so-called Bogomolov-Gieseker type inequality holds for certain stable objects in the derived category. It has been shown to hold for Fano 3-folds of Picard rank one due to the works of Macri, Schmidt and Li. However, Schmidt gave a counter-example for a Fano 3-fold of higher Picard rank. In this talk, I will explain how to modify the original conjectural inequality for general Fano 3-folds and why it holds.
