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Hirzebruch X<sub>y</sub> genera of the Hilbert schemes of surfaces by localization formula

Kefeng Liu Catherine Yan Jian Zhou

Algebraic Geometry mathscidoc:1912.43107

Science in China Series A: Mathematics, 45, (4), 420-431
We use the Atiyah-Bott-Segal-Singer Lefschetz fixed point formula to calculate the Hirzebruch ?<sub>y</sub> genus X<sub>y</sub>(S<sup>[n]</sup>), where S<sup>[n]</sup> is the Hilbert scheme of points of length n of a surface S. Combinatorial interpretation of the weights of the fixed points of the natural torus action on (<sup>2</sup>)<sup>[n]</sup> is used. This is the first step to prove a conjectural formula about the elliptic genus of the Hilbert schemes.
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@inproceedings{kefenghirzebruch,
  title={Hirzebruch X<sub>y</sub> genera of the Hilbert schemes of surfaces by localization formula},
  author={Kefeng Liu, Catherine Yan, and Jian Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111602863682667},
  booktitle={Science in China Series A: Mathematics},
  volume={45},
  number={4},
  pages={420-431},
}
Kefeng Liu, Catherine Yan, and Jian Zhou. Hirzebruch X<sub>y</sub> genera of the Hilbert schemes of surfaces by localization formula. Vol. 45. In Science in China Series A: Mathematics. pp.420-431. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111602863682667.
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