Higher syzygies on abelian surfaces

2016/08/22 by Shin, Jaesun
#14C20 #14K99 #52A10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.06052

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 L² is large. As an application, we improve the existing lower bound of (L²) for higher syzygies of a polarized abelian surface (X,L).

Related

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• A Reider-type theorem for higher syzygies on abelian surfaces
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• Seshadri constants of indecomposable polarized abelian varieties
• Higher syzygies on general polarized abelian varieties of type (1,…,1,d)