Tautological integrals on curvilinear Hilbert schemes

Abstract

We take a new look at the curvilinear Hilbert scheme of points on a smooth projective variety $X$ as a projective completion of the non-reductive quotient of holomorphic map germs from the complex line into $X$ by polynomial reparametrisations. Using an algebraic model of this quotient coming from global singularity theory we develop an iterated residue formula for tautological integrals over curvilinear Hilbert schemes.

Minor corrections+explanatory sections on equivariant duals and localisation from arXiv:1011.4710 are shortened

References in corpus (1)

• Zero dimensional Donaldson-Thomas invariants of threefolds

Cited by in corpus (2)

• Enumeration of rational curves in a moving family of ${\mathbb{P}}^2$
• Counting planar curves in ${\mathbb{P}}^3$ with degenerate singularities