Geodesic
On the Singularity of some Special Components of Springer Fibers
Journal of Lie theory, Tome 21 (2011) no. 1, pp. 205-242.

Voir la notice de l'article provenant de la source Heldermann Verlag

Let V be an n-dimensional C-vector space and let u from V to V be a nilpotent endomorphism. The variety of u-stable complete flags is called the Springer fiber over u. Its irreducible components are parameterized by a set of standard Young tableaux. The Richardson (respectively, Bala-Carter) components of Springer fibers correspond to the Richardson (resp. Bala-Carter) elements of the symmetric group, through Robinson-Schensted correspondence. Every Richardson component is isomorphic to a product of standard flag varieties. By contrast, the Bala-Carter components are very susceptible to be singular. First, we characterize the singular Bala-Carter components in terms of two minimal forbidden configurations. Next, we introduce two new families of components, wider than the families of Bala-Carter components and Richardson components, and both in duality via the tableau transposition. The components in the first family are characterized by the fact that they have a dense orbit of special type under the action of the stabilizer of u, whereas all components in the second family are iterated fiber bundles over projective spaces.
Classification : 14M15, 05E10, 20G05
Mots-clés : Springer fibers, Richardson components, Bala-Carter components, singularity criteria, iterated bundles 
@article{JLT_2011_21_1_JLT_2011_21_1_a9,
     author = {L. Fresse },
     title = {On the {Singularity} of some {Special} {Components} of {Springer} {Fibers}},
     journal = {Journal of Lie theory},
     pages = {205--242},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2011},
     url = {http://geodesic.mathdoc.fr/item/JLT_2011_21_1_JLT_2011_21_1_a9/}
}
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L. Fresse . On the Singularity of some Special Components of Springer Fibers. Journal of Lie theory, Tome 21 (2011) no. 1, pp. 205-242. http://geodesic.mathdoc.fr/item/JLT_2011_21_1_JLT_2011_21_1_a9/