Title:  Bridgeland moduli spaces for Gushel-Mukai threefold and Kuznetsov Fano threefold conjecture

Time: 10:30-11:30am, April 21, 2021

Place: MCM110

Abstract: It is conjectured that the non-trivial components, known as Kuznetsov components of derived category of coherent sheaves on a quartic double solid is equivalent to that of Gushel-Mukai threefold. 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 Kuznetsova components of the special GM threefold. 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.