论文标题
Gushel-Mukai三倍和Kuznetsov的Fano Trix thipold猜想
Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture
论文作者
论文摘要
我们在特殊的平滑gushel-mukai三倍$ x_ {10} $上研究扭曲立方体的Hilbert方案$ \ MATHCAL {H} $。我们证明，如果$ x_ {10} $在特殊的Gushel-mukai三倍之中，则它是一种平稳的投影三倍，而如果$ x_ {10} $不是一般，则是单数。我们在$ x_ {10} $的kuznetsov组件中构建了Bridgeland稳定对象的模量空间的不可约组件，作为$ \ MATHCAL {H} $的分区收缩。我们还在光滑的普通Gushel-mukai三倍上，在$ x_ {10}'$的kuznetsov组件中，在光滑的普通Gushel-mukai三倍上识别圆锥的最小模型（x_ {10}'）$。结果，我们证明了库兹尼托夫的Fano三重猜想是不正确的
We study the Hilbert scheme $\mathcal{H}$ of twisted cubics on a special smooth Gushel-Mukai threefolds $X_{10}$. We show that it is a smooth irreducible projective threefold if $X_{10}$ is general among special Gushel-Mukai threefolds, while it is singular if $X_{10}$ is not general. We construct an irreducible component of a moduli space of Bridgeland stable objects in the Kuznetsov component of $X_{10}$ as a divisorial contraction of $\mathcal{H}$. We also identify the minimal model of Fano surface $\mathcal{C}(X_{10}')$ of conics on a smooth ordinary Gushel-Mukai threefold with moduli space of Bridgeland stable objects in the Kuznetsov component of $X_{10}'$. As a result, we show that the Kuznetsov's Fano threefold conjecture is not true
