Tautological integrals on Hilbert scheme of points II: Geometric subsets

Abstract

We develop a formula for tautological integrals over geometric subsets of the Hilbert scheme of points on complex manifolds. As an illustration of the theory, we derive a new iterated residue formula for the number of nodal curves in sufficiently ample linear systems.

47 pages. Preliminary version, comments are welcome. Survey parts shared with arXiv:2112.15502