A remark on the generic vanishing of Koszul cohomology

Abstract

We give a sufficient condition to study the vanishing of certain Koszul cohomology groups for general pairs $(X,L)\in W_{g,d}^r$ by induction. As an application, we show that to prove the Maximal Rank Conjecture (for quadrics), it suffices to check all cases with the Brill-Noether number $\rho =0$.

7 pages. Comments are welcome