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

Sanghyeon Lee; Jaesun Shin

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arXiv · 1711.03764

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

Sanghyeon Lee·Jaesun Shin

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Abstract

Let $(S,L_{S})$ be a polarized abelian surface, and let $M = c \cdot \pi^*L_S - \alpha \cdot \sum_{i=1}^r E_i$ be a line bundle on ${\rm Bl}_{r}(S)$, where $\pi:{\rm Bl}_{r}(S) \rightarrow S$ is the blow-up of $S$ at $r$ general points with exceptional divisors $E_{1},\dots,E_{r}$. 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.

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Sanghyeon Lee, Jaesun Shin. 2017-11-10. Positivity of line bundles on general blow-ups of abelian surfaces. https://arxiv.org/abs/1711.03764

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