#### Volume 21, issue 5 (2017)

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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
##### Publication
Received: 12 November 2015
Revised: 18 August 2016
Accepted: 11 November 2016
Published: 15 August 2017
Proposed: Lothar Göttsche
Seconded: Frances Kirwan, Dan Abramovich
##### Authors
 Gergely Bérczi Mathematical Institute University of Oxford Andrew Wiles Building OX2 6GG Oxford UK Department of Mathematics ETH Zürich Raemistrasse 101 HG J 16.4 CH-8092 Zürich Switzerland