English

$\mathbb{A}^1$-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 A1\mathbb{A}^1-connected. We obtain this result by classifying vector bundles on a curve upto A1\mathbb{A}^1-concordance. Consequently we classifyPn\mathbb{P}^n- bundles on a curve upto A1\mathbb{A}^1-weak equivalence, extending a result of Asok-Morel. We also give an explicit example of a variety which is A1\mathbb{A}^1-h-cobordant to a projective bundle over P2\mathbb{P}^2 but does not have the structure of a projective bundle over P2\mathbb{P}^2, thus answering a question of Asok-Kebekus-Wendt

Keywords

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