Vol. 14, No. 4, 2020

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The basepoint-freeness threshold and syzygies of abelian varieties

Federico Caucci

Vol. 14 (2020), No. 4, 947–960
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.

Keywords
syzygies, abelian varieties, Fourier–Mukai transform
Mathematical Subject Classification 2010
Primary: 14K05
Secondary: 14C20, 14F17, 14Q20
Milestones
Received: 26 February 2019
Accepted: 6 February 2020
Published: 21 June 2020
Authors
Federico Caucci
Sapienza Università di Roma
Italy