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International audienceThe 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 Poincaré polynomials

On the structure of smooth components of Springer fibers