Higher syzygies on general polarized Abelian varieties of type (1,⋯,1,d)$(1,\dots,1,d)$

Atsushi Ito

Mathematische Nachrichten, 2023, vol. 296, issue 8, 3395-3410

Abstract: In this paper, we show that a general polarized abelian variety (X,L)$(X,L)$ of type (1,⋯,1,d)$(1,\dots ,1,d)$ and dimension g satisfies property (Np)$(N_p)$ if d≥∑i=0g(p+2)i$ d \ge \sum _{i=0}^{g} (p+2)^i$. In particular, the case p=0$p=0$ affirmatively solves a conjecture by Fuentes García on projective normality.

Date: 2023
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