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On the Gauss maps of singular projective varieties. (English) Zbl 1080.14543

Summary: Here we study the dimension \(\delta (m,X)\) of the general fibers of the \(m\)-Gaussian map of a singular \(n\)-dimensional variety \(X \subset {\mathbb{P}}^N\). We show that for all integers \(a,b,c,d\) with \(n \leq a < b \leq c < d \leq N-1\) and \(a + d = b + c\) we have \(\delta (a,X) + \delta (d,X) \geq \delta (b,X) + \delta (c,X)\). If \(\delta (X,N-1)\) is very large we give some classification results which extend to the singular case some results of L. Ein [Invent. Math. 86, 63–74 (1986; Zbl 0603.14025)].

MSC:

14N05 Projective techniques in algebraic geometry
14M15 Grassmannians, Schubert varieties, flag manifolds
14B05 Singularities in algebraic geometry

Citations:

Zbl 0603.14025
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References:

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