Tangent cones of Schubert varieties in Type A

One way to define Type A Schubert varieties is as matrix varieties, that is as a subset of SLn satisfying some extra conditions. The geometry of this variety is tightly connected to the combinatorics of the symmetric group Sn on n letters. Moreover to each element w in S_n there exists one such variety X_w. In this talk I will explain a new approach to a characterization which Schubert varietes X_w and X_v for different w,v in S_n share the same tangent cone at the identity.

This is joint work with Stephane Gaussent (Saint Etienne).

No prior knowledge of Schubert varieties will be assumed.