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We consider the Springer fiber ${\mathcal B}_u$ corresponding to a nilpotentendomorphism $u$ of nilpotent order 2. As a first result, we give a descriptionof the elements of a given component of ${\mathcal B}_u$ which are fixed by theaction of the standard torus relative to some Jordan basis of $u$. By usingthis result, we establish a necessary and sufficient condition of singularityfor the components of ${\mathcal B}_u$.

Singular components of the Springer fiber in the two-columns case