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

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 $K_X^2=p_g-1$.