A remark on the generic vanishing of Koszul cohomology
  We give a sufficient condition to study the vanishing of certain Koszul cohomology groups for general pairs $(X,L)\in W^r_{g,d}$ 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 $\rho=0$. 
Jie Wang
math.AG