Hitching, George H, Hoff, Michael and Newstead, Peter E 
ORCID: 0000-0002-2498-7992
(2020)
Nonemptiness and smoothness of twisted Brill-Noether loci.
Annali di Matematica Pura ed Applicata, 200 (2).
pp. 685-709.
|
Text
Hitching2020_Article_NonemptinessAndSmoothnessOfTwi.pdf - Published version Download (2MB) | Preview |
Abstract
Let $V$ be a vector bundle over a smooth curve $C$. In this paper, we study twisted Brill--Noether loci parametrising stable bundles $E$ of rank $n$ and degree $e$ with the property that $h^0 (C, V \otimes E) \ge k$. We prove that, under conditions similar to those of Teixidor i Bigas and of Mercat, the Brill-Noether loci are nonempty, and in many cases have a component which is generically smooth and of the expected dimension. Along the way, we prove the irreducibility of certain components of both twisted and "nontwisted" Brill--Noether loci. We describe the tangent cones to the twisted Brill-Noether loci. We end with an example of a general bundle over a general curve having positive-dimensional twisted Brill--Noether loci with negative expected dimension.
| Item Type: | Article |
|---|---|
| Additional Information: | 23 pages, typos corrected, new section "Tangent cones to twisted Brill-Noether loci" |
| Uncontrolled Keywords: | math.AG, math.AG, 14H60 (14H51) |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 07 Jul 2020 07:56 |
| Last Modified: | 18 Jan 2023 23:46 |
| DOI: | 10.1007/s10231-020-01009-x |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3093019 |
Dimensions
Dimensions
