Intersection numbers on the relative Hilbert schemes of points on surfaces

Amin Gholampour, Artan Sheshmani

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We study certain top intersection products on the Hilbert scheme of points on a nonsingular surface relative to an effective smooth divisor. We find a formula relating these numbers to the corresponding intersection numbers on the non-relative Hilbert schemes. In particular, we obtain a relative version of the explicit formula found by Carlsson-Okounkov for the Euler class of the twisted tangent bundle of the Hilbert schemes.

Original languageEnglish (US)
Pages (from-to)531-542
Number of pages12
JournalAsian Journal of Mathematics
Volume21
Issue number3
DOIs
StatePublished - 2017
Externally publishedYes

Keywords

  • Donaldson- Thomas invariants
  • Intersection numbers
  • Modular forms
  • Projective surface
  • Relative Hilbert schemes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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