Advanced Studies in Pure Mathematics

Positivity of Thom polynomials and Schubert calculus

Piotr Pragacz

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538623006

Digital Object Identifier
doi:10.2969/aspm/07110419

Mathematical Reviews number (MathSciNet)
MR3644830

Zentralblatt MATH identifier
1378.14057

Subjects
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

Keywords
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

Citation

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. https://projecteuclid.org/euclid.aspm/1538623006


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