STRATIFICATION OF A SINGULAR COMPONENT OF A SPRINGER FIBER OVER x 2 = 0 OF THE SIMPLEST TYPE

Ronit Mansour, Anna Melnikov

Research output: Contribution to journalArticlepeer-review

Abstract

Let x ∈ Mn(K) satisfy x2 = 0. Let Fx be the Springer fiber over x. The components of Fx are labeled by standard Young tableaux with two columns. For a Young tableau T with two columns, one can define a numerical invariant ρ(T). The component FT is singular if and only if ρ(T) ≥ 2. In this paper, we construct the stratification of FT for T with ρ(T) = 2, which reflects also the inner structure of the singular locus, and show that such components have equivalent stratifications if and only if they are isomorphic as algebraic varieties and provide the combinatorial procedure which partitions the set of such components into the classes of isomorphic components. We explain why the stratification of FT for T with ρ(T) ≥ 3 is very complex and does not reflect the inner structure of the singular locus.

Original languageEnglish
JournalTransformation Groups
DOIs
StateAccepted/In press - 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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