报告题目: Kuznetsov's Fano threefold conjectures for quartic double solids and Gushel-Mukai threefolds

报告人：张诗卓（爱丁堡大学博士后）

报告时间：2021年1月8日上午10:00

报告地点：数学研究中心学术报告厅

摘要: It is conjectured that the non-trivial components, known as Kuznetsov components of derived category of coherent sheaves on quartic double solid is equivalent to that of Gushel-Mukai threefolds. I will introduce special Gushel-Mukai threefold X and its Fano scheme of twisted cubics on it and prove it is a smooth irreducible projective threefold when X is general and describe its singularity when X is not general. We will show that it is an irreducible component of Bridgeland moduli space of stable objects of a (-2)-class in the Kuznetsov components of the special GM threefolds. I will show that an irreducible component of Bridgeland moduli space of stable objects of a (-1)-class in the Kuznetsov component of an ordinary GM threefold is the minimal model of Fano surface of conics. As a result, we show the Kuznetsov's Fano threefold conjecture is not true.

                                              数学与统计学院

                                               2021.1.5