$\mathbb{A}^1$-connectedness of moduli of vector bundles on a stacky curve

Sujoy Chakraborty; Saurav Holme Choudhury; Rakesh Pawar

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arXiv · 2609.28203

$\mathbb{A}^1$-connectedness of moduli of vector bundles on a stacky curve

Sujoy Chakraborty·Saurav Holme Choudhury·Rakesh Pawar

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Abstract

Let $\mathfrak{C}$ be a projective stacky curve over an infinite field, together with a generating sheaf $\mathcal{E}$. We consider the moduli stack of $\mathcal{E}$-semistable vector bundles of fixed determinant and multiplicities on $\mathfrak{C}$, and show that the moduli stack of such bundles is $\mathbb{A}^1$-connected. As a consequence, we conclude that the moduli stack of parabolic $α$-semistable vector bundles of fixed determinant and parabolic type on a connected smooth projective curve is $\mathbb{A}^1$-connected.

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BibTeX RIS

Sujoy Chakraborty, Saurav Holme Choudhury, Rakesh Pawar. 2026-09-23. $\mathbb{A}^1$-connectedness of moduli of vector bundles on a stacky curve. https://arxiv.org/abs/2609.28203

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