Back to Algebraic Geometry Seminar: Fall 2015
Algebraic Geometry Seminar
Date: Tuesday, Oct 20, 2015
Time: 3:30PM - 4:30PM
Location: JFB 102
Nils Henry Williams Rasmussen
University of Utah
Title |
Pencils and nets on curves arising from rank 1 torsion free sheaves on K3 surfaces |
Abstract |
Given a K3 surface S, a smooth curve C and a base-point free linear system A on C, there is an associated vector-bundle on S, depending on C and A, called the Lazarsfeld-Mukai vector bundle. For the case when A is a g^1_d or g^2_d for d small enough, we will show how we can use the vector-bundles to construct a rank-1 torsion free sheaf on S where the global sections cut out the divisors of |A|. We also show how these sheaves prove a special case of a conjecture posed by Donagi and Morrison. |
Algebraic Geometry