no. 3
Springer fiber components in the two columns case for types A and D are normal
[Les composantes de fibre de Springer, dans le cas de deux colonnes de types A et D, sont normales]
Bulletin de la Société Mathématique de France, Tome 140 (2012) no. 3, pp. 309-333.

We study the singularities of the irreducible components of the Springer fiber over a nilpotent element N with N 2 =0 in a Lie algebra of type A or D (the so-called two columns case). We use Frobenius splitting techniques to prove that these irreducible components are normal, Cohen-Macaulay, and have rational singularities.

DOI : 10.24033/bsmf.2629
Classification : 14B05, 14N20
Mots clés : Springer fiber, Frobenius splitting, normality, rational resolution, rational singularities 
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     author = {Perrin, Nicolas and Smirnov, Evgeny},
     title = {Springer fiber components in the two columns case for types $A$ and $D$ are normal},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {309--333},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {140},
     number = {3},
     year = {2012},
     doi = {10.24033/bsmf.2629},
     mrnumber = {3059118},
     zbl = {1268.14006},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/bsmf.2629/}
}
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Perrin, Nicolas; Smirnov, Evgeny. Springer fiber components in the two columns case for types $A$ and $D$ are normal. Bulletin de la Société Mathématique de France, Tome 140 (2012) no. 3, pp. 309-333. doi : 10.24033/bsmf.2629. http://www.numdam.org/articles/10.24033/bsmf.2629/

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