Tropical methods for stable octic double planes

TL;DR

This paper demonstrates how tropical geometry and mirror symmetry techniques can be applied to classify and analyze the moduli space of octic double planes, especially focusing on non-Gorenstein cases.

Contribution

It introduces novel applications of tropical and mirror symmetry methods to classify strata in the KSBA moduli space of octic double planes, emphasizing non-Gorenstein surfaces.

Findings

Classification of strata in the moduli space of octic double planes.

Identification of non-Gorenstein stable surfaces within the moduli.

Demonstration of tropical methods' effectiveness in algebraic surface classification.

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.