Gross–Popescu's ideal-generation conjecture for polarized abelian surfaces

Let $(A,L)$ be a polarized abelian surface of type $(1,d)$, where $L$ is very ample and $d\geq 9$. Write the associated embedding as

$$A\subseteq \mathbb{P}(H^0(A,L)).$$

Gross–Popescu's conjecture. The homogeneous ideal of $A$ in this embedding is generated by quadrics and cubics.

The conjecture concerns the equations defining polarized abelian surfaces in projective space. The source proves a generalization using projective normality and states that the corresponding ideal-generation result has three exceptions, but it does not explicitly establish the conjecture in the full stated generality.