[Les composantes de fibre de Springer, dans le cas de deux colonnes de types et , sont normales]
We study the singularities of the irreducible components of the Springer fiber over a nilpotent element with in a Lie algebra of type or (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.
Keywords: Springer fiber, Frobenius splitting, normality, rational resolution, rational singularities
@article{BSMF_2012__140_3_309_0,
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},
year = {2012},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {140},
number = {3},
doi = {10.24033/bsmf.2629},
mrnumber = {3059118},
zbl = {1268.14006},
language = {en},
url = {https://www.numdam.org/articles/10.24033/bsmf.2629/}
}
TY - JOUR AU - Perrin, Nicolas AU - Smirnov, Evgeny TI - Springer fiber components in the two columns case for types $A$ and $D$ are normal JO - Bulletin de la Société Mathématique de France PY - 2012 SP - 309 EP - 333 VL - 140 IS - 3 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/bsmf.2629/ DO - 10.24033/bsmf.2629 LA - en ID - BSMF_2012__140_3_309_0 ER -
%0 Journal Article %A Perrin, Nicolas %A Smirnov, Evgeny %T Springer fiber components in the two columns case for types $A$ and $D$ are normal %J Bulletin de la Société Mathématique de France %D 2012 %P 309-333 %V 140 %N 3 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/bsmf.2629/ %R 10.24033/bsmf.2629 %G en %F BSMF_2012__140_3_309_0
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
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