Gorenstein stable log surfaces with $(K_X+\Lambda)^2=p_g(X,\Lambda)-1$

TL;DR

This paper provides a complete classification of Gorenstein stable log surfaces with a specific relation between their canonical divisor and geometric genus, advancing understanding in algebraic surface classification.

Contribution

It offers a comprehensive classification of Gorenstein stable log surfaces where the square of the canonical divisor plus boundary equals the geometric genus minus one.

Findings

Classification of Gorenstein stable log surfaces with $(K_X+ abla)^2=p_g-1$

Special focus on Gorenstein stable surfaces with $K_X^2=p_g-1$

Advances in the algebraic classification of stable surfaces

Abstract

In this paper, we will give a complete classification of Gorenstein stable log surfaces $(X,\Lambda)$ with $(K_X+\Lambda)^2=p_g(X,\Lambda)-1$, where $p_g(X,\Lambda):=h^0(X,K_X+\Lambda)$. In particular, we classify Gorenstein stable surfaces with $K_X^2=p_g-1$.