𝔸^1-connectedness of moduli of semistable bundles and symplectic bundles on a curve

Abstract

In this note, we show that over a geometrically irreducible smooth projective curve over an infinite field k, the moduli stack of semistable vector bundles of fixed determinant is 𝔸¹-connected if and only if the moduli stack admits a k-rational point. For this we use Langton's elementary modifications for vector bundles at the level of families. In addition, we prove the 𝔸¹-connectedness of the moduli stack of symplectic bundles with forms valued in a fixed line bundle L on a smooth projective curve of genus g ≥ 2 over an infinite field k with C(k)≠ ∅. As an application, we deduce the 𝔸¹-connectedness of moduli stack of quasi-parabolic symplectic vector bundles with forms valued in a fixed line bundle.

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BibTeX RIS

BibTeX

@misc{dubey2026𝔸1connectedness,
  title = {{$\mathbbA^1$-connectedness of moduli of semistable bundles and symplectic bundles on a curve}},
  author = {Umesh V Dubey and Rakesh Pawar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06458},
  eprint = {2610.06458},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06458},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - 𝔸^1-connectedness of moduli of semistable bundles and symplectic bundles on a curve
AU  - Umesh V Dubey
AU  - Rakesh Pawar
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.06458
UR  - https://arxiv.org/abs/2610.06458
AB  - In this note, we show that over a geometrically irreducible smooth projective curve over an infinite field k, the moduli stack of semistable vector bundles of fixed determinant is 𝔸^1-connected if and only if the moduli stack admits a k-rational point. For this we use Langton's elementary modifications for vector bundles at the level of families. In addition, we prove the 𝔸^1-connectedness of the moduli stack of symplectic bundles with forms valued in a fixed line bundle L on a smooth projective curve of genus g ≥ 2 over an infinite field k with C(k)≠ ∅. As an application, we deduce the 𝔸^1-connectedness of moduli stack of quasi-parabolic symplectic vector bundles with forms valued in a fixed line bundle.
ER  -

𝔸¹-connectedness of moduli of semistable bundles and symplectic bundles on a curve

Abstract

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