Higher syzygies on abelian surfaces

Abstract

Based on the theory of an infinitesimal Newton-Okounkov body, we extend the results of Lazarsfeld-Pareschi-Popa on abelian surfaces. Moreover, we show that the higher syzygies of $(X,L)$ are completely determined by its Seshadri constant when $L^2$ is large. As an application, we improve the existing lower bound of $(L^2)$ for higher syzygies of a polarized abelian surface $(X,L)$.

14 pages, There was a critical error in the proof of Lemma 3.1 in version 1, so we removed some related results. We modified and added some results

References in corpus (1)

• Local positivity of linear series on surfaces

Cited by in corpus (1)

• Extended Okounkov bodies and multi-point Seshadri constants