Bridgeland moduli spaces for Gushel-Mukai threefold and Kuznetsov Fano threefold conjecture
[Math. Dept.]
March 19, 2021 16:00-18:00
W303 School of Mathematics
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 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 Kuznetsov 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.
SUPPORTED BY
School of Mathematics, Sichuan University