## Kyoto Journal of Mathematics

### Critical $k$-very ampleness for abelian surfaces

#### Abstract

Let $(S,L)$ be a polarized abelian surface of Picard rank $1$, 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 $n\gt 1$. As a by-product, we calculate the walls in the Bridgeland stability space for certain Chern characters.

#### Article information

Source
Kyoto J. Math., Volume 56, Number 1 (2016), 33-47.

Dates
Revised: 22 May 2014
Accepted: 3 December 2014
First available in Project Euclid: 15 March 2016

https://projecteuclid.org/euclid.kjm/1458047877

Digital Object Identifier
doi:10.1215/21562261-3445147

Mathematical Reviews number (MathSciNet)
MR3479317

Zentralblatt MATH identifier
1342.14024

#### Citation

Alagal, Wafa; Maciocia, Antony. Critical $k$ -very ampleness for abelian surfaces. Kyoto J. Math. 56 (2016), no. 1, 33--47. doi:10.1215/21562261-3445147. https://projecteuclid.org/euclid.kjm/1458047877

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