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PreprintarXiv licencearXiv

The canonical class and Chern character operators on Hilbert schemes of points

  • Wei-Ping Li
  • Zhongyi Shi
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Abstract

Let X be a smooth projective complex surface. We obtain explicit formulas for the Chern character operators on the Hilbert schemes of points X[n] in terms of Nakajima operators, determining in particular the coefficients of the terms involving the canonical class KX and its square. Consequently, the cohomology ring structure of the Hilbert scheme is determined. As an application, we give an alternative proof of the action of the affine Yangian Yt1,t2(gl̂1) on the cohomological Fock space ℍX = ⨁n≥ 0 H*(X[n],ℚ).

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Cite

BibTeXRIS
BibTeX
@misc{li2026canonical,
  title = {{The canonical class and Chern character operators on Hilbert schemes of points}},
  author = {Wei-Ping Li and Zhongyi Shi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14491},
  eprint = {2610.14491},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14491},
}
RIS
TY  - UNPB
TI  - The canonical class and Chern character operators on Hilbert schemes of points
AU  - Wei-Ping Li
AU  - Zhongyi Shi
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2610.14491
UR  - https://arxiv.org/abs/2610.14491
AB  - Let X be a smooth projective complex surface. We obtain explicit formulas for the Chern character operators on the Hilbert schemes of points X^[n] in terms of Nakajima operators, determining in particular the coefficients of the terms involving the canonical class K_X and its square. Consequently, the cohomology ring structure of the Hilbert scheme is determined. As an application, we give an alternative proof of the action of the affine Yangian Y_t_1,t_2(gl̂_1) on the cohomological Fock space ℍ_X = ⨁_n≥ 0 H^*(X^[n],ℚ).
ER  -