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June 2013 Tautological module and intersection theory on Hilbert schemes of nodal curves
Ziv Ran
Asian J. Math. 17(2): 193-264 (June 2013).

Abstract

This paper presents the rudiments of Hilbert-Mumford Intersection (HMI) theory: intersection theory on the relative Hilbert scheme of a family of nodal (or smooth) curves, over a base of arbitrary dimension. We introduce an additive group of geometric cycles, called ’tautological module’, generated by diagonal loci, node scrolls, and twists thereof. We determine recursively the intersection action on this group by the discriminant (big diagonal) divisor and all its powers. We show that this suffices to determine arbitrary polynomials in Chern classes, in particular Chern numbers, for the tautological vector bundles on the Hilbert schemes, which are closely related to enumerative geometry of families of nodal curves.

Citation

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Ziv Ran. "Tautological module and intersection theory on Hilbert schemes of nodal curves." Asian J. Math. 17 (2) 193 - 264, June 2013.

Information

Published: June 2013
First available in Project Euclid: 8 November 2013

zbMATH: 1282.14097
MathSciNet: MR3078931

Subjects:
Primary: 14H99, 14N99

Rights: Copyright © 2013 International Press of Boston

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Vol.17 • No. 2 • June 2013
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