J. Austral. Math. Soc.  72 (2002), 119-130
On the Gauss maps of singular projective varieties

E. Ballico
  Department of Mathematics
  University of Trento
  38050 Povo (TN)
  Italy
  ballico@science.unitn.it


Abstract
Here we study the dimension $\delta (m,X)$ of the general fibers of the  m-Gaussian map of a singular  n-dimensional variety $X \subset {\bf {P}}^N$. We show that for all integers  a,  b,  c,  d with $n \le a < b \le c < d \le N-1$ and  a + d = b + c we have $\delta (a,X) + \delta (d,X) \ge \delta (b,X) + \delta (c,X)$. If $\delta (X,N-1)$ is very large we give some classification results which extend to the singular case some results of Ein.
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