Algebraic Geometry Seminar

Title

Syzygies of subcanonical subschemes. Abstract: I will describe joint work with D. Eisenbud and Ch. Walter on resolutions by vector bundles. The idea is that coherent sheaves on projective space which are symmetric in a suitable sense have symmetric vector bundle resolutions. This generalizes results on surfaces with even sets of nodes, theta characteristics of plane curves, self-linked space curves, and recent results of Catanese, Kleiman-Lipman-Ulrich, Walter and others. I will also describe a structure result for Gorenstein subcanonical projective subschemes of codimension 3, and construct examples of smooth codimension 3 subcanonical varieties which are not Pfaffian (a projective subscheme of codimension 3 is Pfaffian if it is the degeneracy locus of a skew-symmetric morphism f : E^* --> E(t) with E a vector bundle of odd rank.)

Abstract