Tautological integrals on curvilinear Hilbert schemes

Bérczi, Gergely¹

¹ 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

Geometry & topology, Tome 21 (2017) no. 5, pp. 2897-2944.

Résumé

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.

Détail

DOI : 10.2140/gt.2017.21.2897

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

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