$\mathbb{A}^1$-connectivity of moduli of vector bundles on a curve
| Autor: | Hogadi, Amit, Yadav, Suraj |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this note we prove that the moduli stack of vector bundles on a curve, with a fixed determinant is $\mathbb{A}^1$-connected. We obtain this result by classifying vector bundles on a curve upto $\mathbb{A}^1$-concordance. Consequently we classify$\mathbb{P}^n$- bundles on a curve upto $\mathbb{A}^1$-weak equivalence, extending a result of Asok-Morel. We also give an explicit example of a variety which is $\mathbb{A}^1$-h-cobordant to a projective bundle over $\mathbb{P}^2$ but does not have the structure of a projective bundle over $\mathbb{P}^2$, thus answering a question of Asok-Kebekus-Wendt Comment: 10 pages. Minor corrections and modifications. Results unchanged. Final Version. Accepted for publication in Journal of Inst. of Math of Jussieu |
| Databáze: | arXiv |
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