A moduli space of stable sheaves on a cubic threefold

Abstract

In this paper, we prove that the moduli space ${\overline{M}}_X(v)$ of Gieseker semistable sheaves on a smooth cubic threefold $X$ with Chern character $v=(4,-H,-\frac{5}{6}{H}^2,\frac{1}{6}{H}^3)$ is non-empty, smooth and irreducible of dimension $8$. Moreover, we show that ${\overline{M}}_X(v)$ is isomorphic to a Bridgeland moduli space in the Kuznetsov component of $X$ and provide a set-theoretic description of it.

arXiv commentfinal form to appear in Math. Nachr