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Cohomological Hall algebras and Quot schemes of curves

  • Shivang Jindal
  • Woonam Lim
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Abstract

We study cohomological Hall algebras of curves and their actions on the homology of Quot schemes. We introduce the virtual homology of Quot schemes and show that it is preserved by both creation and annihilation actions. We prove that the torsion CoHA is isomorphic to a shuffle algebra and, equivalently, to a braided symmetric algebra associated with a Yang-Baxter operator. We use this description to determine the ideal of tautological relations for punctual Quot schemes and obtain a new basis for their cohomology rings. Finally, we introduce a universal way to double the torsion CoHA and show that it acts naturally on the virtual homology of Quot schemes of arbitrary type.

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Cite

BibTeXRIS
BibTeX
@misc{jindal2026cohomological,
  title = {{Cohomological Hall algebras and Quot schemes of curves}},
  author = {Shivang Jindal and Woonam Lim},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08323},
  eprint = {2609.08323},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08323},
}
RIS
TY  - UNPB
TI  - Cohomological Hall algebras and Quot schemes of curves
AU  - Shivang Jindal
AU  - Woonam Lim
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08323
UR  - https://arxiv.org/abs/2609.08323
AB  - We study cohomological Hall algebras of curves and their actions on the homology of Quot schemes. We introduce the virtual homology of Quot schemes and show that it is preserved by both creation and annihilation actions. We prove that the torsion CoHA is isomorphic to a shuffle algebra and, equivalently, to a braided symmetric algebra associated with a Yang-Baxter operator. We use this description to determine the ideal of tautological relations for punctual Quot schemes and obtain a new basis for their cohomology rings. Finally, we introduce a universal way to double the torsion CoHA and show that it acts naturally on the virtual homology of Quot schemes of arbitrary type.
ER  -