ON BLOWIN-UP OF POLARIZED SURFACES

摘要

Let (S,L) be a polarized surface and left π:S → S be the blow-up at r points p_1,...p_r on S.Set L~=π*L-∑aiEi, where ai's are positive integers and Ei's are the (-1)-curves over pi. We cinsider whether L~ is ample or not if pi's are in a general position. The cases of sectional genus two are studied especially precisely.