THE COMPONENTS OF THE SINGULAR LOCUS OF A COMPONENT OF A SPRINGER FIBER OVER x 2 = 0

Ronit Mansour; Anna Melnikov

doi:10.1007/s00031-020-09621-0

THE COMPONENTS OF THE SINGULAR LOCUS OF A COMPONENT OF A SPRINGER FIBER OVER x ² = 0

Ronit Mansour, Anna Melnikov

Department of Mathematics

University of Haifa

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

Abstract

For x ∈ End(Kⁿ) satisfying x² = 0 let F_x be the variety of full flags stable under the action of x (Springer fiber over x). The full classification of the components of F_x according to their smoothness was provided in [4] in terms of both Young tableaux and link patterns. Moreover in [2] the purely combinatorial algorithm to compute the singular locus of a singular component of F_x is provided. However, this algorithm involves the computation of the graph of the component, and the complexity of computations grows very quickly, so that in practice it is impossible to use it. In this paper, we construct another algorithm, giving all the components of the singular locus of a singular component F_σ of F_x in terms of link patterns constructed straightforwardly from the link pattern of σ.

Original language	American English
Pages (from-to)	597-633
Number of pages	37
Journal	Transformation Groups
Volume	27
Issue number	2
DOIs	https://doi.org/10.1007/s00031-020-09621-0
State	Published - 2020

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology

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title = "THE COMPONENTS OF THE SINGULAR LOCUS OF A COMPONENT OF A SPRINGER FIBER OVER x 2 = 0",

abstract = "For x ∈ End(Kn) satisfying x2 = 0 let Fx be the variety of full flags stable under the action of x (Springer fiber over x). The full classification of the components of Fx according to their smoothness was provided in [4] in terms of both Young tableaux and link patterns. Moreover in [2] the purely combinatorial algorithm to compute the singular locus of a singular component of Fx is provided. However, this algorithm involves the computation of the graph of the component, and the complexity of computations grows very quickly, so that in practice it is impossible to use it. In this paper, we construct another algorithm, giving all the components of the singular locus of a singular component Fσ of Fx in terms of link patterns constructed straightforwardly from the link pattern of σ.",

author = "Ronit Mansour and Anna Melnikov",

note = "Funding Information: RONIT MANSOUR is supported by ISF grant 797/14. Publisher Copyright: {\textcopyright} 2020, Springer Science+Business Media, LLC, part of Springer Nature.",

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THE COMPONENTS OF THE SINGULAR LOCUS OF A COMPONENT OF A SPRINGER FIBER OVER x ² = 0

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