Advanced Studies in Pure Mathematics

Positivity of Thom polynomials and Schubert calculus

Piotr Pragacz

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We describe the positivity of Thom polynomials of singularities of maps, Lagrangian Thom polynomials and Legendrian Thom polynomials. We show that these positivities come from Schubert calculus.

Article information

Schubert Calculus — Osaka 2012, H. Naruse, T. Ikeda, M. Masuda and T. Tanisaki, eds. (Tokyo: Mathematical Society of Japan, 2016), 419-451

Received: 9 April 2013
Revised: 20 March 2014
First available in Project Euclid: 4 October 2018

Permanent link to this document euclid.aspm/1538623006

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05E05: Symmetric functions and generalizations 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15] 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 14N10: Enumerative problems (combinatorial problems) 14N15: Classical problems, Schubert calculus 32S20: Global theory of singularities; cohomological properties [See also 14E15] 55R40: Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20] 57R45: Singularities of differentiable mappings

positivity Grassmannian Lagrangian Grassmannian Schubert class Schur function $\widetilde{Q}$-function singularity class Thom polynomial vector bundle generated by its global sections ample vector bundle positive polynomial nonnegative cycle


Pragacz, Piotr. Positivity of Thom polynomials and Schubert calculus. Schubert Calculus — Osaka 2012, 419--451, Mathematical Society of Japan, Tokyo, Japan, 2016. doi:10.2969/aspm/07110419.

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