New perspective on categorical Torelli problems for del Pezzo threefold
报告人： 张诗卓 研究员 中科院数学所晨兴数学中心
时间： 2024年7月31日下午13:00-17:00
地点： 海纳苑2幢102
报告人简介：张诗卓于2019年毕业于印第安纳大学，后于爱丁堡大学，德国波恩马普所，法国图卢兹数学所，德国Hausdorff 数学研究所，美国加州大学伯克利分校MSRI数学研究所做博后，目前在中科院数学所晨兴数学中心访问。张诗卓博士的研究方向是代数簇的凝聚层导出范畴，Bridgeland 稳定性条件以及在Fano簇上模空间以及hyperkahler簇的应用，最近两年主要研究Fano簇的范畴化Torelli问题。研究工作已经在Math Ann, JMPA, Journal of London Math Society, Math Z, Math research letter等杂志上发表或者接受待发表。
题目：New perspective on categorical Torelli problems for del Pezzo threefold
摘要：Let Y be a del Pezzo threefold of Picard rank one and degree d\geq 2. We provide a Brill-Noether reconstruction of those del Pezzo threefolds as a subscheme of a Bridgeland moduli spaces in their Kuznetsov components. We show that any exact equivalence between their Kuznetsov components preserves a distinguished object up to some natural auto-equivalences of the Kuznetsov component. As a result, we give a uniform proof of categorical Torelli theorem for them. Further more, we compute the group of auto-equivalences of their Kuznetsov component by extending the exact equivalences to the whole bounded derived categories. Then I will also talk about the group of auto-equivalences of Kuznetsov component of index one prime Fano threefold where a different techniques are used. As an application we show that the group of automorphism of index one genus 8 prime Fano threefold is isomorphic to that of associated Phaffian cubic threefold, which is not known in the literature. If time permits I will also talk about an application on equivariant categorical Torelli theorem for a cubic threefold with geometric involution.
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联系人： 刘伟华