Frontiers of Mathematics in China >

2017 , Vol. 12 >Issue 5: 1247 - 1264

DOI: https://doi.org/10.1007/s11464-017-0686-4

RESEARCH ARTICLE

Generating series of intersection numbers on Hilbert schemes of points

  • Zhilan WANG , 1 ,
  • Jian ZHOU 2
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  • 1. Department of Mathematics, China University of Mining and Technology, Beijing 100083, China
  • 2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received date: 08 Jul 2016

Accepted date: 07 Apr 2017

Published date: 30 Sep 2017

Copyright

2017 Higher Education Press and Springer-Verlag GmbH Germany
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Abstract

We compute some generating series of integrals related to tautological bundles on Hilbert schemes of points on surfaces S[n], including the intersection numbers of two Chern classes of tautological bundles, and the Euler characteristics of Λ_yTS[n]. We also propose some related conjectures, including an equivariant version of Lehn’s conjecture.

Key words： Hilbert scheme; tautological sheaf; intersection number

Cite this article

Zhilan WANG , Jian ZHOU . Generating series of intersection numbers on Hilbert schemes of points[J]. Frontiers of Mathematics in China, 2017 , 12(5) : 1247 -1264 . DOI: 10.1007/s11464-017-0686-4

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