  Gross and Popescu conjectured that the homogeneous ideal of an embedded
$(1,d)$-polarized abelian surface is generated by quadrics and cubics for
$d\geq 9$. We prove this using the projective normality of the embedding. It
follows that the homogeneous ideal of an abelian surface embedded by a complete
linear system is generated by quadrics and cubics, with three exceptions.
