Smooth Schubert varieties and generalized Schubert polynomials in algebraic cobordism of Grassmannians

Jens Hornbostel; Nicolas Perrin

doi:10.2140/pjm.2018.294.401

Smooth Schubert varieties and generalized Schubert polynomials in algebraic cobordism of Grassmannians

Jens Hornbostel
, Nicolas Perrin

Bergische Universität Gesamthochschule Wuppertal
Laboratoire de Mathématiques de Versailles

Research output: Contribution to journal › Article › peer-review

Abstract

We provide several ingredients towards a generalization of the Littlewood- Richardson rule from Chow groups to algebraic cobordism. In particular, we prove a simple product formula for multiplying classes of smooth Schubert varieties with any Bott-Samelson class in algebraic cobordism of Grassmannians. We also establish some results for generalized Schubert polynomials for hyperbolic formal group laws.

Original language	English
Pages (from-to)	401-422
Number of pages	22
Journal	Pacific Journal of Mathematics
Volume	294
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2018.294.401
Publication status	Published - 1 Jan 2018
Externally published	Yes

Keywords

Cobordism
Generalized cohomology
Grassmannian
Schubert calculus

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10.2140/pjm.2018.294.401

Cite this

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abstract = "We provide several ingredients towards a generalization of the Littlewood- Richardson rule from Chow groups to algebraic cobordism. In particular, we prove a simple product formula for multiplying classes of smooth Schubert varieties with any Bott-Samelson class in algebraic cobordism of Grassmannians. We also establish some results for generalized Schubert polynomials for hyperbolic formal group laws.",

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AU - Hornbostel, Jens

AU - Perrin, Nicolas

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N2 - We provide several ingredients towards a generalization of the Littlewood- Richardson rule from Chow groups to algebraic cobordism. In particular, we prove a simple product formula for multiplying classes of smooth Schubert varieties with any Bott-Samelson class in algebraic cobordism of Grassmannians. We also establish some results for generalized Schubert polynomials for hyperbolic formal group laws.

AB - We provide several ingredients towards a generalization of the Littlewood- Richardson rule from Chow groups to algebraic cobordism. In particular, we prove a simple product formula for multiplying classes of smooth Schubert varieties with any Bott-Samelson class in algebraic cobordism of Grassmannians. We also establish some results for generalized Schubert polynomials for hyperbolic formal group laws.

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KW - Generalized cohomology

KW - Grassmannian

KW - Schubert calculus

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JF - Pacific Journal of Mathematics

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Smooth Schubert varieties and generalized Schubert polynomials in algebraic cobordism of Grassmannians

Abstract

Keywords

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