Doubly indexed flag variety and fixed point set of a partial flag variety

Abstract: We define a variety of doubly indexed flags, this is a smooth, projective variety, and we describe it as an iterated over Grassmannian varieties. On the other hand, we consider the variety of partial flags which are stabilized by a given nilpotent endomorphism. We partition this variety into locally closed subvarieties which are vector bundles over varieties of the aforedmentioned type.

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Grassmannians, Schubert varieties, flag manifolds (14M15) Coadjoint orbits; nilpotent varieties (17B08)

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