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  in terms of both Young tableaux and link patterns. Moreover in  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.
Bibliographical noteFunding Information:
RONIT MANSOUR is supported by ISF grant 797/14.
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ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology