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
of equioriented quivers of type A.