Thom series of contact singularities


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.


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