Abstract
In this paper we prove the following results: let X be a complex torus and M a line bundle on X; if M satisfies Property N 1 of Green, then, for every q ≥ 1, the line bundle Mq satisfies Property Nq (precisely we prove a more general result concerning not necessarily linear syzygies); this is a particular case of a conjecture formulated in Citation[1]; finally we prove that, if M satisfies Property N 0 and s ≥ 2, then the ring ⊕ n H 0(Y, Msn ) is Koszul.
ACKNOWLEDGMENTS
I warmly thank G. Pareschi for an useful conversation and in particular for explaining me how Lazarsfeld simplified the proof of the main result of Kempf' work Citation[9].