arXiv subjects

Saurav Holme Choudhury

Publications and source records attributed to Saurav Holme Choudhury.

3 recordsLinked to original sources

arXiv2026

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

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.

math.AG↗

arXiv2026

$\mathbb{A}^1$--connectedness of moduli stack of semi-stable and parabolic semi-stable vector bundles over a curve

Let $C$ be an irreducible smooth projective curve of genus $g\geq 2$ over an algebraically closed field. We prove that the moduli stack of semi-stable vector bundles on $C$ of fixed rank and determinant is $\mathbb{A}^1$--connected. We also show that the moduli stack of quasi-parabolic vector bundles with a fixed determinant and a given quasi-parabolic data along a set of points in $C$ is $\mathbb{A}^1$-connected. Moreover, for small and generic weights $\boldsymbolα$ with $\gcd(n, °L) = 1$, the open substack of $\boldsymbolα$-semistable parabolic vector bundles is also $\mathbb{A}^1$-connected.

math.AG↗

arXiv2023

Stratified bundles on the Hilbert Scheme of $n$ points

Let $k$ be an algebraically closed field of characteristic $p > 3$ and $S$ be a smooth projective surface over $k$ with $k$-rational point $x$. For $n \geq 2$, let $S^{[n]}$ denote the Hilbert scheme of $n$ points on $S$. In this note, we compute the fundamental group scheme $π^{\textrm{alg}}(S^{[n]}, \tilde{nx})$ defined by the Tannakian category of stratified bundles on $S^{[n]}$.

math.AG↗