Critical k-Very Ampleness for Abelian Surfaces

Antony Maciocia, Wafa Alagal

Research output: Contribution to journalArticlepeer-review

Abstract

Let $(S,L)$ be a $(1,d)$-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.
Original language English 33-47 Kyoto journal of mathematics 56 1 15 Mar 2016 https://doi.org/10.1215/21562261-3445147 Published - 30 Apr 2016

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