On the GIT quotient space of quintic surfaces

Gallardo, Patricio

doi:10.1090/tran/7493

On the GIT quotient space of quintic surfaces
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Trans. Amer. Math. Soc. 371 (2019), 4251-4276 Request permission

Abstract:

We describe the GIT compactification for the moduli space of smooth quintic surfaces in ${\mathbb {P}^{3}}$. In particular, we show that a normal quintic surface with at worst isolated double points or minimal elliptic singularities is stable. We also describe the boundary of the GIT quotient, and we discuss the stability of the nonnormal surfaces.

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