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PreprintarXiv licencearXiv

Tangent bundles of Quot schemes of vector bundles on curves

  • Ashima Bansal
  • Supravat Sarkar
  • Shivam Vats
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Abstract

For a vector bundle E on a smooth projective curve C, one defines the Quot scheme Q:=Qd(E,C) parametrizing subsheaves of E having length d torsion quotients. We describe the indecomposable components of the tangent bundle TQ of Q, thus characterizing when TQ is indecomposable. We also characterize when TQ is simple; in fact, we completely describe the endomorphism rings of the indecomposable components of TQ. As an application, we determine when two products of such Quot schemes can be isomorphic.

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Cite

BibTeXRIS
BibTeX
@misc{bansal2026tangent,
  title = {{Tangent bundles of Quot schemes of vector bundles on curves}},
  author = {Ashima Bansal and Supravat Sarkar and Shivam Vats},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21287},
  eprint = {2609.21287},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21287},
}
RIS
TY  - UNPB
TI  - Tangent bundles of Quot schemes of vector bundles on curves
AU  - Ashima Bansal
AU  - Supravat Sarkar
AU  - Shivam Vats
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21287
UR  - https://arxiv.org/abs/2609.21287
AB  - For a vector bundle E on a smooth projective curve C, one defines the Quot scheme Q:=Q_d(E,C) parametrizing subsheaves of E having length d torsion quotients. We describe the indecomposable components of the tangent bundle T_Q of Q, thus characterizing when T_Q is indecomposable. We also characterize when T_Q is simple; in fact, we completely describe the endomorphism rings of the indecomposable components of T_Q. As an application, we determine when two products of such Quot schemes can be isomorphic.
ER  -