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Here we study the dimension δ(m, X) of the general fibers of the m-Gaussian map of a singular n-dimensional variety X ⊂ Pn. We show that for all integers a, b, c, d with n ≦ a < b ≦ c < d ≦ N − 1 and a + d = b + c we have δ (a, X) + δ(d, X) > δ(b, X) + δ(c, X). If δ(X, N − 1) is very large we give some classification results which extend to the singular case some results of Ein.

Let G be a unitary group of rank one over a non-archimedean local field K (whose residue field has a characteristic ≠ 2). We consider the action of G on the projective plane. A G(K) equivariant map from the set of points in the projective plane that are semistable for every maximal K split torus in G to the set of convex subsets of the building of G(K) is constructed. This map gives rise to an equivariant map from the set of points that are stable for every maximal K split torus to the building. Using these maps one describes a G(K) invariant pure affinoid covering of the set of stable points. The reduction of the affinoid covering is given.

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On the Gauss maps of singular projective varieties

On the action of the unitary group on the projective plane over a local field

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182 results in 14Mxx

On the Gauss maps of singular projective varieties

On the action of the unitary group on the projective plane over a local field