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PreprintCC0arXiv

Torelli theorem for the product of moduli spaces of vector bundles over a curve

  • Indranil Biswas
  • Arijit Dey
  • Anubhab Pahari
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Abstract

We prove a Torelli-type theorem for a product of the moduli spaces of semistable vector bundles over smooth projective curves of genus g ≥ 4. A similar result is proved for the product of the moduli stacks of semistable vector bundles. This is proved using a decomposition theorem for the product of the normal projective varieties with Picard rank one and discrete Picard group. As an application, we compute the automorphism group of the product of the moduli spaces and moduli stacks.

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Cite

BibTeXRIS
BibTeX
@misc{biswas2026torelli,
  title = {{Torelli theorem for the product of moduli spaces of vector bundles over a curve}},
  author = {Indranil Biswas and Arijit Dey and Anubhab Pahari},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10764},
  eprint = {2609.10764},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10764},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Torelli theorem for the product of moduli spaces of vector bundles over a curve
AU  - Indranil Biswas
AU  - Arijit Dey
AU  - Anubhab Pahari
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10764
UR  - https://arxiv.org/abs/2609.10764
AB  - We prove a Torelli-type theorem for a product of the moduli spaces of semistable vector bundles over smooth projective curves of genus g ≥ 4. A similar result is proved for the product of the moduli stacks of semistable vector bundles. This is proved using a decomposition theorem for the product of the normal projective varieties with Picard rank one and discrete Picard group. As an application, we compute the automorphism group of the product of the moduli spaces and moduli stacks.
ER  -