2007/09/08 by Piotr Pragacz, Pragacz, Piotr, Andrzej Weber +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.0709.1191
openalex publication_date 2007/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize the notion of Thom polynomials from singularities of maps between two complex manifolds to invariant cones in representations, and collections of vector bundles. We prove that the generalized Thom polynomials, expanded in the products of Schur functions of the bundles, have nonnegative coefficients. For classical Thom polynomials associated with maps of complex manifolds, this gives an extension of our former result for stable singularities to nonnecessary stable ones. We also discuss some related aspects of Thom polynomials, which makes the article expository to some extent.