Algebraic Geometry Seminar
Yusuf Mustopa
U. of Michigan
Subordinate Loci on Symmetric Products and Syzygies of Points
Abstract: The dth symmetric product C_d of a smooth projective curve C is a
smooth projective variety which encodes the "degree-d aspect" of the
geometry of C. The subordinate loci on C_d associated to linear series on C
encode the degree-d aspect of maps from C to projective space. In this
talk, I will discuss how these loci govern the cone of effective divisors of
C_d, how some natural divisors on C_d may be characterized as subordinate
loci associated to higher-rank vector bundles, and also a conjectural
description of the effective cone of C_d when C is a general curve of genus
g and d is at least (g/2)+1.
Thursday February 18, 2010 at 4:00 PM in SEO 636