Some remarks on Fano threefolds of index two and stability conditions

Laura Pertusi; Song Yang

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arXiv · 2004.02798

Some remarks on Fano threefolds of index two and stability conditions

Laura Pertusi·Song Yang

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Abstract

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, Macr\`i 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 $\mathsf{Ku}(X)$.

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Laura Pertusi, Song Yang. 2020-04-06. Some remarks on Fano threefolds of index two and stability conditions. https://arxiv.org/abs/2004.02798

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