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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
References
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