On the moduli space of quintic surfaces

On the moduli space of quintic surfaces

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Patricio Gallardo, Stony Brook University
Fine Hall 322

We describe the use of GIT and stable replacement for studying the geometry of a special compactification of the moduli space of smooth quintic surfaces, the KSBA compactification. In particular we discuss the interplay between non-log-canonical singularities and boundary divisors. Our presentation will be enriched by drawing analogies with similar phenomena on the moduli space of curves of genus three.