Tropical methods for stable octic double planes

Abstract

This paper has been written to illustrate the power of techniques from tropical geometry and mirror symmetry for studying the KSBA moduli space of surfaces on or near the Noether line. We focus on the moduli space of octic double planes ($K^2=2$, $p_g=3$) and use methods from tropical and toric geometry to classify the strata corresponding to normal KSBA-stable surfaces, focusing on the non-Gorenstein case.

51 pages, 19 figures; v2 results strengthened, exposition streamlined, title made more specific; v3 fixed a gap in the classification; v4 some clarifications after referee report