Gorenstein stable surfaces with $K_X^2 =1$ and $ \chi(\mathcal O_X) =2$

TL;DR

This paper classifies Gorenstein stable surfaces with specific invariants, detailing their moduli space structure and contributing to the understanding of algebraic surface classification.

Contribution

It provides a detailed classification of Gorenstein stable surfaces with $K_X^2=1$ and $ chi( O_X)=2$, expanding the knowledge of their moduli space.

Findings

Identification of several strata in the moduli space

Detailed descriptions of surface families within these strata

Advancement in the classification of algebraic surfaces

Abstract

We classify - as far as possible - Gorenstein stable surfaces with $K_X^2 = 1$ and $\chi(\mathcal O_X) = 2$, describing several strata in the moduli space quite in detail.