A generalization of Castelnuovo regularity to Grassmann manifolds
A coherent algebraic sheaf on a projective space has an associated numerical invariant called its Castelnuovo regularity. It provides a measure of the degrees of syzygies in its minimal free resolution. Here we extend the theory to sheaves on Grassmann manifolds. We show that the new definition of regularity coincides with the old one if the Grassmannian is a projective space, and establish some of its formal properties. We give concrete estimates on regularity for some special types of subschemes of the Grassmannian; viz., smooth curves, Fano schemes and Schubert varieties. ^
Major Professor: Donu V. B. Arapura, Purdue University.