Surfaces on the Severi line in positive characteristic

Abstract

Let k \mathbf {k} be an algebraically closed field, a minimal surface X X over k \mathbf {k} of maximal Albanese dimension is called on the Severi line if the ‘Severi equality’: K X 2 = 4 χ ( O X ) K^2_X=4\chi (\mathcal {O}_X) holds. We prove that X X is on the Severi line if and only if its canonical model X c a n X_{\mathrm {can}} admits a flat double cover over an Abelian surface.