Abstract
The aim of this paper is to study the structure of the smooth irreducible components of the Springer fibers associated to nilpotent endo-morphisms 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 Poincare polynomials.
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