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                Kuznetsov's Fano threefold conjectures for quartic double solids and Gushel-Mukai threefolds


                主讲人:张诗卓,University of Edinburgh




                内容介绍: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.