Complex surfaces polarized by an ample and spanned line bundle of genus three

Abstract

Let X be a complex connected projective nonsingular algebraic surface endowed with an ample line bundle L, which is spanned by its global sections. Pairs (X, L) as above, with sectional genus g(X, L)=1+(L·(K X ⊗L))/2=3 are classified by means of the main techniques of adjunction theory.