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 $K_X^2=p_g-1$.

To appear in Communications in Algebra