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arXiv · 1401.4046

Critical k-Very Ampleness for Abelian Surfaces

Wafa Alagal·Antony Maciocia
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Abstract

Let $(S,L)$ be a polarized abelian surface of Picard rank one and let $\phi$ be the function which takes each ample line bundle $L'$ to the least integer $k$ such that $L'$ is $k$-very ample but not $(k+1)$-very ample. We use Bridgeland's stability conditions and Fourier-Mukai techniques to give a closed formula for $\phi(L^n)$ as a function of $n$ showing that it is linear in $n$ for $n>1$. As a byproduct, we calculate the walls in the Bridgeland stability space for certain Chern characters.

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Wafa Alagal, Antony Maciocia. 2014-01-16. Critical k-Very Ampleness for Abelian Surfaces. https://doi.org/10.1215/21562261-3445147

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