Stability of hypersurface sections of quadric threefolds

Abstract

Let $S$ be a complete intersection of a smooth quadric 3-fold $Q$ and a hypersurface of degree $d$ in ${\mathbb{P}}^4$. In this paper we analyze GIT stability of $S$ with respect to the natural $G=SO(5,\mathbb{C})$-action. We prove that if $d\ge 4$ and $S$ has at worst semi-log canonical singularities then $S$ is $G$-stable. Also, we prove that if $d\ge 3$ and $S$ has at worst semi-log canonical singularities then $S$ is $G$-semistable.

10 pages, SCIENCE CHINA Mathematics (to appear)

References in corpus (1)

• Finite Hilbert stability of (bi)canonical curves