Critical k-Very Ampleness for Abelian Surfaces

Abstract

Let $(S,L)$ be a polarized abelian surface of Picard rank one and let $\varphi$ be the function which takes each ample line bundle $L^{\prime }$ to the least integer $k$ such that $L^{\prime }$ 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 $\varphi (L^n)$ 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.

13 pages. Two references added to papers by Terakawa. The authors are grateful to Kota Yoshioka for pointing these out. A number of corrections and some parts rewritten to help with clarity (thanks to the referee). References updated. Paper to appear in Kyoto J. Math

References in corpus (1)

• Computing the Walls Associated to Bridgeland Stability Conditions on Projective Surfaces

Cited by in corpus (1)

• Towards generic base-point-freeness for hyperkähler manifolds of generalized Kummer type