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On the Gauss maps of singular projective varieties

Part of: Local theory Projective and enumerative geometry Special varieties

Published online by Cambridge University Press:  09 April 2009

E. Ballico
E. Ballico
Affiliation:
Department of Mathematics, University of Trento, 38050 Povo (TN), Italy e-mail: ballico@science.unitn.it
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Abstract

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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.

Keywords

Gauss mapprojective varietyGrassmannianGauss map for singular varietiestangencycontact locusdual varietyadjunction mapping

MSC classification

Secondary: 14N05: Projective techniques 14M15: Grassmannians, Schubert varieties, flag manifolds 14B05: Singularities
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 1 , February 2002 , pp. 119 - 130
Copyright
Copyright © Australian Mathematical Society 2002

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