Volume 21, issue 5 (2017)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
Tautological integrals on curvilinear Hilbert schemes

Gergely Bérczi

Geometry & Topology 21 (2017) 2897–2944
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 nonreductive 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.

Keywords
Hilbert scheme of points, curve counting, Göttsche formula, tautological integrals, nonreductive quotients, equivariant localisation, iterated residue
Mathematical Subject Classification 2010
Primary: 14C05, 14N10, 55N91