Harvard-MIT Algebraic Geometry Seminar
        	    February 19, 2002 at 3:00 p.m.
			   Harvard Room 507



               Stable bundles, difference varieties and
             divisors on moduli spaces of pointed curves


                  Gavril Farkas (Univ. of Michigan)



Abstract: 

We do global calculations on moduli spaces of pointed curves to
compute the graded Betti numbers of general sets of points on any
nonhyperelliptic canonically embedded curve C. It turns out that these
results have surprising connections with moduli spaces of stable
vector bundles on curves and geometric divisors on moduli spaces of
pointed curves.

Among other things we prove that for any canonically embedded curve C,
all exterior powers of the universal quotient on C have a theta
divisor which is identified with a difference variety in the Jacobian
of C. These vector bundles are of great interest since Green's
Conjecture on syzygies of canonical curves boils down to computing the
dimensions of their spaces of sections.

This is joint work with M. Mustata and M. Popa.