Singular components of the Springer fiber in the two-columns case

Details Singular components of the Springer fiber in the two-columns case Singular components of the Springer fiber in the two-columns case

2008-03-14

arxiv.org/abs/0803.2188v2

Ann. Inst. Fourier (Grenoble) 59 (2009) 2429-2444

Mathematics

Algebraic Geometry

11 pages

Scientific paper

We consider the Springer fiber ${\mathcal B}_u$ corresponding to a nilpotent endomorphism $u$ of nilpotent order 2. As a first result, we give a description of the elements of a given component of ${\mathcal B}_u$ which are fixed by the action of the standard torus relative to some Jordan basis of $u$. By using this result, we establish a necessary and sufficient condition of singularity for the components of ${\mathcal B}_u$.

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