Seminar| Institute of Mathematical Sciences
Time：Monday, December 28th, 2020, 15:00-16:00
Location：Room 408, IMS
Speaker: Shizhuo Zhang, University of Edinburgh
Abstract: It is conjectured that the non-trivial components, known as Kuznetsov components of derived category of coherent sheaves on every 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.