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 P-4. We analyze GIT stability of S with respect to the natural G = SO(5, C)-action. We prove that if d >= 4 and S has at worst semi-log canonical singularities then S is G-stable. Also, we prove that if d >= 3 and S has at worst semi-log canonical singularities then S is G-semistable.