Singular divisors and syzygies of polarized abelian threefolds

Research output: Working paper/Preprint › Preprint

Authors

  • Victor Lozovanu

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Original languageEnglish
Number of pages28
Publication statusE-pub ahead of print - 23 Mar 2018

Abstract

We provide numerical conditions for a polarized abelian threefold (A,L) to have simple syzygies, in terms of property (Np) and the vanishing of Koszul cohomology groups Kp,1. We rely on a reduction method of Lazarsfeld-Pareschi-Popa, convex geometry of Newton-Okounkov bodies, inversion of adjunction techniques from work on Fujita's conjecture, and the use of differentiation by Ein-Lazarsfeld-Nakamye. As a by-product, we construct effective divisors in any ample class of high self-intersetion, whose singularities are all concentrated on an abelian subvariety. This can be seen as the dual picture considered by Ein-Lazarsfeld for theta divisors.

Cite this

Singular divisors and syzygies of polarized abelian threefolds. / Lozovanu, Victor.
2018.

Research output: Working paper/Preprint › Preprint

Lozovanu, V. (2018). Singular divisors and syzygies of polarized abelian threefolds. Advance online publication.
Lozovanu V. Singular divisors and syzygies of polarized abelian threefolds. 2018 Mar 23. Epub 2018 Mar 23.
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