Syzygies of abelian varieties

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Asymptotic syzygies of algebraic varieties (2011, background): “For abelian varieties, Pareschi [24] established analogous bounds that do not depend on the dimension.”
Regularity on abelian varieties I (2001, methodology): “with index 0, which follows as a consequence of [ Pa ] Theorem 3.8.”
Regularity on abelian varieties II: Basic results on linear series and defining equations (2001, methodology): “ Theorem [M2], [Ke1]) For k ≥ 4, the ideal of X in the embedding given be Ak is generated by quadrics. In the embedding given by A3 it is generated by quadrics and cubics. (8)(Lazarsfeld’s Conjecture [Pa], extending results of Kempf [Ke2]) Ap+3 satisﬁes property Np (extending (5) and (7)). (9)(Khale”
Regularity on Abelian Varieties III: Relationship with Generic Vanishing and Applications (2008, background): “t∗ xF) −→ H0(E⊗t∗ xF) are surjective for all x∈ Xif we have the following vanishing: hi(φ∗ Θ((−1 X) ∗E⊗O (−Θ))b⊗F(−Θ)) = 0, ∀i>0. REGULARITY AND GENERIC VANISHING ON ABELIAN VARIETIES 23 Proof. By [Pa] Theorem 3.1, all the multiplication maps in the statement are surjective if the skew-Pontrjagin”