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.
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In memory of Ernest Borisovich Vinberg
RONIT MANSOUR is supported by ISF grant 797/14.
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MANSOUR, R., MELNIKOV, A. THE COMPONENTS OF THE SINGULAR LOCUS OF A COMPONENT OF A SPRINGER FIBER OVER x2 = 0. Transformation Groups 27, 597–633 (2022). https://doi.org/10.1007/s00031-020-09621-0
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DOI: https://doi.org/10.1007/s00031-020-09621-0