On the structure of Thom polynomials of singularities

Details On the structure of Thom polynomials of singularities On the structure of Thom polynomials of singularities

2007-08-22

arxiv.org/abs/0708.3068v1

Mathematics

Algebraic Geometry

Scientific paper

Thom polynomials of singularities express the cohomology classes dual to singularity submanifolds. A stabilization property of Thom polynomials is known classically, namely that trivial unfolding does not change the Thom polynomial. In this paper we show that this is a special case of a product rule. The product rule enables us to calculate the Thom polynomials of singularities if we know the Thom polynomial of the product singularity. As a special case of the product rule we define a formal power series (Thom series, Ts_Q) associated with a commutative, complex, finite dimensional local algebra Q, such that the Thom polynomial of {\em every} singularity with local algebra Q can be recovered from Ts_Q.

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