Singularities and divisors in the moduli space of surfaces

Abstract: The KSBA moduli space of stable surfaces (surfaces with slc singularities and ample canonical class) is a natural compactification of Gieseker's moduli space of surfaces of general type. In contrast with the moduli space of curves, very little is known about the birational geometry of KSBA moduli spaces; indeed, there are very few examples of divisors in KSBA moduli spaces. I will give an example of a divisor in the moduli space of quintic surfaces corresponding to surfaces with cyclic quotient singularities. I also discuss joint work with Giancarlo Urz\'ua where we give bounds that help to narrow the search.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

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