论文标题
关于索引的三倍和稳定性条件的三倍
Some remarks on Fano threefolds of index two and stability conditions
论文作者
论文摘要
我们证明，对于由Bayer，Lahoz，Lahoz，Macrì和Stellari构建的稳定性条件，在Kuznetsov组件$ \ mathsf {ku}（x）$中，Picard排名第一和索引二的理想线条是稳定的对象。当$ x $是立方三倍时，我们表明$ \ mathsf {ku}（x）$的Serre函数可保留这些稳定性条件。作为一个应用程序，我们在$ \ Mathsf {ku}（x）$中获得了稳定对象的非空模型空间的平滑度。当$ x $是四分之一的双实固体时，我们描述了$ \ mthsf {ku}（x）$上稳定性歧管稳定性条件的连接组件。
We prove that ideal sheaves of lines in a Fano threefold $X$ of Picard rank one and index two are stable objects in the Kuznetsov component $\mathsf{Ku}(X)$, with respect to the stability conditions constructed by Bayer, Lahoz, Macrì and Stellari, giving a modular description to the Hilbert scheme of lines in $X$. When $X$ is a cubic threefold, we show that the Serre functor of $\mathsf{Ku}(X)$ preserves these stability conditions. As an application, we obtain the smoothness of non-empty moduli spaces of stable objects in $\mathsf{Ku}(X)$. When $X$ is a quartic double solid, we describe a connected component of the stability manifold parametrizing stability conditions on $\mathsf{Ku}(X)$.
