The basepoint-freeness threshold and syzygies of abelian varieties

Abstract

We show how a natural constant introduced by Jiang and Pareschi for a polarized abelian variety encodes information about the syzygies of the section ring of the polarization. As a particular case this gives a quick and characteristic-free proof of Lazarsfeld's conjecture on syzygies of abelian varieties, originally proved by Pareschi in characteristic zero.

arXiv comment14 pages, final version, to appear on Algebra and Number Theory

References in corpus (3)

• Singular divisors and syzygies of polarized abelian threefolds
• Cohomological rank functions on abelian varieties
• Buser-Sarnak invariant and projective normality of abelian varieties

Cited by in corpus (5)

• Chern degree functions
• Higher syzygies on general polarized abelian varieties of type $(1,\dots ,1,d)$
• M-regularity of $\mathbb{Q}$-twisted sheaves and its application to linear systems on abelian varieties
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• Jets-separation thresholds, Seshadri constants and higher Gauss-Wahl maps on abelian varieties