Compact moduli of elliptic surfaces with a multiple fiber

Abstract

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. Particular emphasis is placed on rational elliptic surfaces without a section and on Dolgachev surfaces. Our main goal is to understand the limit surfaces when a multiple fiber degenerates into an additive type singular fiber, via $\mathbb{Q}$-Gorenstein smoothings of slc surfaces.

arXiv comment20 pages, final version, to appear in Algebra & Number Theory. This version includes revisions to the moduli constructions in Section 3 and additional details in Sections 4 and 5