Positivity of line bundles on general blow-ups of abelian surfaces

摘要

Let (S, L-s) be a polarized abelian surface, and let M = c . pi* L-s - alpha . Sigma(i=1) (r) be a line bundle on Bl(r) (S), where pi : Bl(r)(S) -> S is the blow-up of S at r general points with exceptional divisors E-1, . . . , E-r . In this paper, we provide a criterion for k-very ampleness of M. Also, we deal with the case when S is an arbitrary surface of Picard number one with a numerically trivial canonical divisor. (C) 2019 Elsevier Inc. All rights reserved.