Volume 21, issue 5 (2017)

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Tautological integrals on curvilinear Hilbert schemes

Gergely Bérczi

Geometry & Topology 21 (2017) 2897–2944

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.

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Hilbert scheme of points, curve counting, Göttsche formula, tautological integrals, nonreductive quotients, equivariant localisation, iterated residue
Mathematical Subject Classification 2010
Primary: 14C05, 14N10, 55N91
Received: 12 November 2015
Revised: 18 August 2016
Accepted: 11 November 2016
Published: 15 August 2017
Proposed: Lothar Göttsche
Seconded: Frances Kirwan, Dan Abramovich
Gergely Bérczi
Mathematical Institute
University of Oxford
Andrew Wiles Building
OX2 6GG Oxford
Department of Mathematics
ETH Zürich
Raemistrasse 101
HG J 16.4
CH-8092 Zürich