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The flag variety of a complex reductive linear algebraic group   $G$   is by definition the quotient   $G/B$   by a Borel subgroup. It can be regarded as the set of Borel subalgebras of   ${\rm Lie}(G)$  . Given a nilpotent element   $e$   in   ${\rm Lie}(G)$  , one calls Springer fiber the subvariety formed by the Borel subalgebras which   $e$   belongs to. Springer fibers have in general a complicated structure (not irreducible, singular). Nevertheless, a theorem by De Concini, Lusztig, and Procesi asserts that when   $G$   is classical, a Springer fiber can always be paved by finitely many subvarieties isomorphic to affine spaces. In this paper, we study varieties generalizing the Springer fibers in two ways: being contained in a partial flag variety   $G/P$   (the quotient by a parabolic subgroup, instead of a Borel subgroup) and defined by a more general belonging condition (in terms of an ideal of   ${\rm Lie}(P))$  . These varieties arise, for instance, as fibers of resolutions of nilpotent orbit closures. The main result of the paper is a generalization of De Concini, Lusztig, and Procesi's theorem to this context.Communicated by Corrado de Concini

Existence of Affine Pavings for Varieties of Partial Flags Associated to Nilpotent Elements