A generalization of Castelnuovo regularity to Grassmann varieties

Using the Beilinson–Kapranov spectral sequence, we define Castelnuovo regularity for a coherent sheaf on a Grassmann variety. We show that many formal properties of regularity over projective spaces continue to hold in this generality and derive concrete bounds on the degrees of defining equations for subvarieties of the Grassmannian. Received: 23 November 1999 / Revised version: 12 March 2000