Kuznetsov's Fano threefold conjectures for quartic double solids and Gushel-Mukai threefolds
Speaker: Zhang Shizhuo, professor from University of Edinburgh
Time: 10 am, December 31st, 2020
Place: Room 332, No. 3 Building
Sponsor: SHNU College of Mathematics and Mechanical Engienering
About: It is conjectured that the non-trivial components, known as Kuznetsov componentsof derived category of coherent sheaves on every quartic double solid isequivalent to that of Gushel-Mukai threefold. I will introduce special Gushel-Mukai threefold X and its Fano scheme of twisted cubics on it and proveit is a smooth irreducible projective threefold when X is general and describeits 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 minimalmodel of Fano surface of conics. As a result, we show the Kuznetsov's Fano threefold conjecture is not true.