Projectivity of the moduli space of vector bundles on a curve
Algebraic Geometry
2023-05-01 v1
Abstract
We discuss the projectivity of the moduli space of semistable vector bundles on a curve of genus . This is a classical result from the 1960s, obtained using geometric invariant theory. We outline a modern approach that combines the recent machinery of good moduli spaces with determinantal line bundle techniques. The crucial step producing an ample line bundle follows an argument by Faltings with improvements by Esteves-Popa. We hope to promote this approach as a blueprint for other projectivity arguments.
Keywords
Cite
@article{arxiv.2206.06195,
title = {Projectivity of the moduli space of vector bundles on a curve},
author = {Jarod Alper and Pieter Belmans and Daniel Bragg and Jason Liang and Tuomas Tajakka},
journal= {arXiv preprint arXiv:2206.06195},
year = {2023}
}
Comments
31 pages, expository article, accepted for publication in Stacks Project Expository Collection, to be published by Cambridge University Press, London Mathematical Society Lecture Note Series