|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Global Brill–Noether
theory over the Hurwitz space
Eric Larson, Hannah Larson and Isabel Vogt |
|
Geometry & Topology 29 (2025) 193–257
|
|
DOI: 10.2140/gt.2025.29.193
|
Abstract |
|
Let be a curve of genus . A fundamental problem in the theory of algebraic curves is to understand maps of specified degree . When is general, the moduli space of such maps is well understood by the main theorems of Brill–Noether theory. Despite much study over the past three decades, a similarly complete picture has proved elusive for curves of fixed gonality. Here we complete such a picture, by proving analogs of all of the main theorems of Brill–Noether theory in this setting. As a corollary, we prove a conjecture of Eisenbud and Schreyer regarding versal deformation spaces of vector bundles on . |
Keywords
Brill–Noether theory, Hurwitz space
|
Mathematical Subject Classification
Primary: 14H51
|
References |
Publication
Received: 8 January 2023
Accepted: 25 February 2023
Published: 1 January 2025
Proposed: Jim Bryan
Seconded: Richard P Thomas, Mark Gross
|
Authors |
| Eric Larson | |
| Department of Mathematics Brown University Providence, RI United States |
|
| Hannah Larson | |
| Department of Mathematics University of California, Berkeley Berkeley, CA United States |
|
| Isabel Vogt | |
| Department of Mathematics Brown University Providence, RI United States |
|
| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
This article is currently available only to readers at paying institutions. If enough institutions subscribe to this Subscribe to Open journal for 2025, the article will become Open Access in early 2025. Otherwise, this article (and all 2025 articles) will be available only to paid subscribers.
