Syzygies of Polarized Abelian Surfaces: A Reider-Type Criterion

Let $(X,L)$ be a polarized complex abelian surface with $L^2=2d$. We establish a Reider-type criterion for Property $N_p$. If $d\geq7$, then $L$ satisfies Property $N_0$ if and only if there is no elliptic curve $E\subseteq X$ with $L\cdot E\leq2$, with one explicitly described exception. If $p\geq1