Thom series of contact singularities

Abstract

Thom polynomials measure how global topology forces singularities. The power of Thom polynomials predestine them to be a useful tool not only in differential topology, but also in algebraic geometry (enumerative geometry, moduli spaces) and algebraic combinatorics. The main obstacle of their widespread application is that only a few, sporadic Thom polynomials have been known explicitly. In this paper we develop a general method for calculating Thom polynomials of singularities. Along the way, relations with the equivariant geometry of (punctual, local) Hilbert schemes and with iterated residue identities are revealed.

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Authors

L. M. Fehér

Department of Analysis
Eötvös University Budapest
1053 Hungary

R. Rimányi

Department of Mathematics
University of North Carolina at Chapel Hill
Chapel Hill, NC 27599-3250