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On the structure of smooth components of Springer fibers


Authors: Lucas Fresse, Anna Melnikov and Sammar Sakas-Obeid
Journal: Proc. Amer. Math. Soc. 143 (2015), 2301-2315
MSC (2010): Primary 14M15, 17B08, 05E10
DOI: https://doi.org/10.1090/S0002-9939-2015-12460-4
Published electronically: January 14, 2015
MathSciNet review: 3326013
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Abstract: The aim of this paper is to study the structure of the smooth irreducible components of the Springer fibers associated to nilpotent endomorphisms of nilpotency order 2. Relying on its combinatorial interpretation in terms of standard Young tableaux, we show that each smooth component has a structure of iterated bundle of Grassmannian varieties, with explicit base. Using this description, we then classify the smooth components according to their Poincaré polynomials.


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Additional Information

Lucas Fresse
Affiliation: Université de Lorraine, CNRS, Institut Élie Cartan de Lorraine, UMR 7502, Vandoeuvre-lès-Nancy, F-54506, France
Email: lucas.fresse@univ-lorraine.fr

Anna Melnikov
Affiliation: Department of Mathematics, University of Haifa, Haifa 31905, Israel
Email: melnikov@math.haifa.ac.il

Sammar Sakas-Obeid
Affiliation: Department of Mathematics, University of Haifa, Haifa 31905, Israel
Email: obsamar@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2015-12460-4
Keywords: Components of a Springer fiber, Grassmannian varieties, flag manifolds, iterated bundles, Betti numbers
Received by editor(s): September 20, 2013
Received by editor(s) in revised form: December 15, 2013
Published electronically: January 14, 2015
Additional Notes: The first author was partially supported by ISF grant 882/10
Communicated by: Lev Borisov
Article copyright: © Copyright 2015 American Mathematical Society