Yusuf Mustopa : Subordinate Loci on Symmetric Products and Syzygies of Points

Posted by , part of the Algebraic Geometry Seminar.

At

Feb. 18, 2010, 4 p.m.

In

SEO 636

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.