Singular divisors and syzygies of polarized abelian threefolds

2018/03/23 by Victor Lozovanu, Lozovanu, Victor · 2 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1803.08780

Abstract

We provide numerical conditions for a polarized abelian threefold (A,L) to have simple syzygies, in terms of property (N_p) and the vanishing of Koszul cohomology groups K_p,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.

Citations

• On the projective normality of complete linear series on an algebraic curve
• The generic Green–Lazarsfeld Secant Conjecture

Cited by

• The Infinitesimal Torelli Theorem for hypersurfaces in abelian varieties
• Multiplicities of irreducible theta divisors

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