学术报告（张诗卓 1.5）

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. 
据猜测，在每个四次双体上，相应的导出范畴的非平凡分支（称为库兹涅佐夫分支）等价于古谢尔-向井三维簇。 我将介绍特殊的古谢尔-向井三维簇X及其扭曲三次曲线的法诺概型，并证明当X为一般时它是光滑的不可约射影三维簇，并描述当X不为一般时其奇异性。 我们将证明它是特殊古谢尔-向井三维库兹涅佐夫分支（-2）类稳定对象的布里奇兰德模空间的不可约分支。 我将证明，普通古谢尔-向井的三维簇库兹涅佐夫分支中（-1）类稳定对象的布里奇兰德模空间的不可约分支是圆锥曲线的法诺曲面的极小模型。 结果，我们证明了库兹涅佐夫的法诺三维簇猜想是不正确的。