论文标题
Brill - Kuznetsov组件的非理论和精制的分类Torelli定理，用于索引一个fano三倍
Brill--Noether theory for Kuznetsov components and refined categorical Torelli theorems for index one Fano threefolds
论文作者
论文摘要
我们通过一个统一的论点表明，每个索引一个prime fano三倍的$ x $属$ g \ geq 6 $可以重建为brill-bridgeland moduli在kuznetsov组件$ \ mathcal $ \ mathcal {k} u（x）u（x）$中的稳定物体内的稳定物体内部的bridgeland locus。作为一个应用程序，我们以$ x $的形式证明了精制的分类torelli定理，并计算每个fano的纤维纤维，每三倍的三倍$ g \ geq 7 $就某些与子类别$ \ langle \ langle \ langle \ mathcal \ mathcal \ Mathcal {O} _x \ rangle^_x \ rangle^} $相关的粘合对象而言。这统一了Mukai，Brambilla-Faenzi，Debarre-Iliev-Manivel，Faenzi-Verra，Iliev-Markushevich-Tikhomirov和Kuznetsov的结果。
We show by a uniform argument that every index one prime Fano threefold $X$ of genus $g\geq 6$ can be reconstructed as a Brill--Noether locus inside a Bridgeland moduli space of stable objects in the Kuznetsov component $\mathcal{K}u(X)$. As an application, we prove refined categorical Torelli theorems for $X$ and compute the fiber of the period map for each Fano threefold of genus $g\geq 7$ in terms of a certain gluing object associated with the subcategory $\langle \mathcal{O}_X \rangle^{\perp}$. This unifies results of Mukai, Brambilla-Faenzi, Debarre-Iliev-Manivel, Faenzi-Verra, Iliev-Markushevich-Tikhomirov and Kuznetsov.
