On the GIT Quotient Space of Quintic Surfaces

Abstract

We describe the GIT compactification for the moduli space of smooth quintic surfaces in projective space. In particular, we show that a normal quintic surface with at worst an isolated double point or a minimal elliptic singularity is stable. We also describe the boundary of the GIT quotient, and we discuss the stability of the non-normal surfaces.

arXiv comment25 pages, 2 figure, 1 Table. Some sections have been substantially changed following suggestions of the referee