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PreprintCC BY 4.0arXiv

𝔸1-connectedness of moduli of vector bundles on a stacky curve

  • Sujoy Chakraborty
  • Saurav Holme Choudhury
  • Rakesh Pawar
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Abstract

Let C be a projective stacky curve over an infinite field k with the coarse space C, a geometrically connected smooth projective curve, together with a generating sheaf ℰ on C. We consider the moduli stack of ℰ-semistable vector bundles of fixed determinant and multiplicities on C, and show that it is 𝔸1-connected if and only if it admits a k-rational point. We show that this holds whenever genus of C is at least $2$ and C(k)≠ ∅. As a consequence, we conclude that, for any system of weights α, the moduli stack of parabolic α-semistable vector bundles of fixed determinant and quasi-parabolic data on a geometrically connected smooth projective curve is 𝔸1-connected.

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Cite

BibTeXRIS
BibTeX
@misc{chakraborty2026𝔸1connectedness,
  title = {{$\mathbbA^1$-connectedness of moduli of vector bundles on a stacky curve}},
  author = {Sujoy Chakraborty and Saurav Holme Choudhury and Rakesh Pawar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.28203},
  eprint = {2609.28203},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28203},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - 𝔸^1-connectedness of moduli of vector bundles on a stacky curve
AU  - Sujoy Chakraborty
AU  - Saurav Holme Choudhury
AU  - Rakesh Pawar
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.28203
UR  - https://arxiv.org/abs/2609.28203
AB  - Let C be a projective stacky curve over an infinite field k with the coarse space C, a geometrically connected smooth projective curve, together with a generating sheaf ℰ on C. We consider the moduli stack of ℰ-semistable vector bundles of fixed determinant and multiplicities on C, and show that it is 𝔸^1-connected if and only if it admits a k-rational point. We show that this holds whenever genus of C is at least $2$ and C(k)≠ ∅. As a consequence, we conclude that, for any system of weights α, the moduli stack of parabolic α-semistable vector bundles of fixed determinant and quasi-parabolic data on a geometrically connected smooth projective curve is 𝔸^1-connected.
ER  -