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In this paper, we show that a general polarized abelian variety $(X,L)$ oftype $(1,\dots,1,d)$ 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 aconjecture by L. Fuentes Garc\'{\i}a on projective normality.

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