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We consider the Springer fiber over a nilpotent endomorphism. Fix a Jordanbasis and consider the standard torus relative to this. We deal with theproblem to describe the flags fixed by the torus which belong to a givencomponent of the Springer fiber. We solve the problem in the hook, two-row andtwo-column cases. We provide two main characterizations which are common to thethree cases, and which involve dominance relations between Young diagrams andcombinatorial algorithms. Then, for these three cases, we deduce topologicalproperties of the components and their intersections.

A unified approach on Springer fibers in the hook, two-row and two-column cases