Compact moduli of elliptic surfaces with a multiple fiber

Motivated by Miranda and Ascher-Bejleri’s works on compactifications of the moduli space of rational elliptic surfaces with a section, we study constructions and boundaries of compact moduli spaces of elliptic surfaces with a multiple fiber.

In a joint work with Donggun Lee, we propose an approach to understanding the limit surfaces when a multiple fiber degenerates into an additive type singular fiber, via Q-Gorenstein smoothings of slc surfaces. And in ongoing work with Dori Bejleri and Donggun Lee, we study compact moduli spaces of the rational elliptic surfaces of index 2 and of Enriques surfaces with bisections using the theory of twisted stable maps.