$\mathbb{A}^1$-connectivity of moduli of vector bundles on a curve
Algebraic Geometry
2022-12-15 v2
Abstract
In this note we prove that the moduli stack of vector bundles on a curve, with a fixed determinant is -connected. We obtain this result by classifying vector bundles on a curve upto -concordance. Consequently we classify- bundles on a curve upto -weak equivalence, extending a result of Asok-Morel. We also give an explicit example of a variety which is -h-cobordant to a projective bundle over but does not have the structure of a projective bundle over , thus answering a question of Asok-Kebekus-Wendt
Cite
@article{arxiv.2110.05799,
title = {$\mathbb{A}^1$-connectivity of moduli of vector bundles on a curve},
author = {Amit Hogadi and Suraj Yadav},
journal= {arXiv preprint arXiv:2110.05799},
year = {2022}
}
Comments
10 pages. Minor corrections and modifications. Results unchanged. Final Version. Accepted for publication in Journal of Inst. of Math of Jussieu