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

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