# Abstract Jesus Martinez Garcia

**Jesus Martinez Garcia ** will speak on

** Moduli space of cubic surfaces and their anticanonical divisors**

Abstract: We study compactifications log pairs (X,D) where X is a hypersurface in projective space of some fixed degree and D is a hyperplane section. Geometric Invariant Theory is known to provide a finite number of possible compactifications of such pairs, depending on one parameter. Any two such compactifications are related by birational transformations. We describe an algorithm to study the stability of these pairs, and apply our algorithm to the case of cubic surfaces. Finally, we relate this compactifications to the (conjectural) moduli space of pairs (X,D) where X admits a Kaehler-Einstein metric with singularities along D. We show that any such pair is an element of our moduli and that there is a naturally defined line bundle coming from the geometry which polarizes our compactifications.

This is joint work with Patricio Gallardo (University of Georgia) and Cristiano Spotti (Aarhus University).