Ricerc@Sapienza

Linear degenerate flag varieties are degenerations of flag varieties as quiver Grassmannians.
For type A flag varieties, we obtain characterizations of flatness, irreducibility and
normality of these degenerations via rank tuples. Some of them are shown to be isomorphic
to Schubert varieties and can be realized as highest weight orbits of partially degenerate
Lie algebras, generalizing the corresponding results on degenerate flag varieties. To study
normality, cell decompositions of quiver Grassmannians are constructed in a wider context

Quiver Grassmannians are projective varieties parametrizing subrepresentations
of given dimension in a quiver representation. We define a class of quiver Grassmannians
generalizing those which realize degenerate flag varieties. We show that each irreducible
component of the quiver Grassmannians in question is isomorphic to a Schubert variety.We
give an explicit description of the set of irreducible components, identify all the Schubert
varieties arising, and compute the Poincar´e polynomials of these quiver Grassmannians.