Intersection numbers on the relative Hilbert schemes of points on surfaces

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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
JournalAsian Journal of Mathematics
Issue number3
StatePublished - 2017

Bibliographical note

Revised version according to referee's corrections, 13 pages, To appear in Asian. J. Math. (2016)

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