Asian Journal of Mathematics
Volume 21 (2017)
Intersection numbers on the relative Hilbert schemes of points on surfaces
Pages: 531 – 542
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.
relative Hilbert schemes, intersection numbers, projective surface, Donaldson–Thomas invariants, modular forms
2010 Mathematics Subject Classification
14C05, 14C17, 14D21, 14F43
Paper received on 31 July 2015.