Event

Talk
Brill-Noether theory for vector bundles with fixed determinant
Peter Newstead (Liverpool)
2 Nov 2011, 15:30

In the Brill-Noether theory of stable vector bundles, there is a natural definition of expected dimension, although this cannot always be attained when the rank is greater than 1. For fixed determinant, there is an obvious lower bound on the dimension of components given by subtracting g from the bound for variable determinant. However, for rank 2 and canonical determinant, the bound cannot be attained and there is an alternative natural definition, which is attained in most (probably all) cases. Very recently Osserman has obtained results for other determinants. The main purpose of the talk is to show that in some cases, Osserman's bounds can be attained. The natural context is that of coherent systems. This is joint work with Grzegorczyk.

Related to:

• Alexander Schmitt