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arXiv · 2310.16950

Stability manifolds of Kuznetsov components of prime Fano threefolds

Changping Fan·Zhiyu Liu·Songtao Kenneth Ma
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Abstract

Let $X$ be a cubic threefold, quartic double solid or Gushel--Mukai threefold, and $\mathcal{K}u(X)\subset \mathrm{D}^b(X)$ be its Kuznetsov component. We show that a stability condition $\sigma$ on $\mathcal{K}u(X)$ is Serre-invariant if and only if its homological dimension is at most $2$. As a corollary, we prove that all Serre-invariant stability conditions on $\mathcal{K}u(X)$ form a contractible connected component of the stability manifold.

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Changping Fan, Zhiyu Liu, Songtao Kenneth Ma. 2023-10-25. Stability manifolds of Kuznetsov components of prime Fano threefolds. https://arxiv.org/abs/2310.16950

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