Kyoto Journal of Mathematics

Critical k-very ampleness for abelian surfaces

Wafa Alagal and Antony Maciocia

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Let (S,L) be a polarized abelian surface of Picard rank 1, and let ϕ 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 ϕ(Ln) as a function of n, showing that it is linear in n for n>1. As a by-product, we calculate the walls in the Bridgeland stability space for certain Chern characters.

Article information

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

Received: 11 March 2014
Revised: 22 May 2014
Accepted: 3 December 2014
First available in Project Euclid: 15 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14C20: Divisors, linear systems, invertible sheaves
Secondary: 14D22: Fine and coarse moduli spaces 14K99: None of the above, but in this section

Abelian surface Bridgeland stability moduli spaces very ample


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.

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