On blowing-up of polarized surfaces

抄録

Let (S, L) be a polarized surface and let π:˜{S}→ S be the blow-up at r points p₁, ..., p_r on S. Set \displaystyle ˜{L}=π^*L-∑ a_iE_i, where a_i's are positive integers and E_i's are the (-1)-curves over p_i. We consider whether ˜{L} is ample or not if p_i's are in a general position. The cases of sectional genus two are studied especially precisely.