Dually degenerate varieties and the generalization of a theorem of Griffiths-Harris

Authors

Maks A. Akivis, Jerusalem College of Technology
Vladislav V. Goldberg, New Jersey Institute of Technology

Document Type

Article

Publication Date

5-1-2005

Abstract

The dual variety X * for a smooth n-dimensional variety X of the projective space P^N is the set of tangent hyperplanes to X. In the general case, the variety X * is a hypersurface in the dual space (P ^N)*. If dim∈X *N with a degenerate Gauss map of rankr. For such a variety, in the general case, the dimension of its dual variety X * is N-l-1, where l=n-r, and X is dually degenerate if dim∈X *N is dually degenerate if and only if all its second fundamental forms are singular. The authors generalize this theorem for a variety X ⊂ double struck P sign^N with a degenerate Gauss map of rankr. © Springer 2005.

Identifier

17444394786 (Scopus)

Publication Title

Acta Applicandae Mathematicae

External Full Text Location

https://doi.org/10.1007/s10440-004-7029-7

ISSN

01678019

First Page

249

Last Page

265

Issue

3

Volume

86

Recommended Citation

Akivis, Maks A. and Goldberg, Vladislav V., "Dually degenerate varieties and the generalization of a theorem of Griffiths-Harris" (2005). Faculty Publications. 19703.
https://digitalcommons.njit.edu/fac_pubs/19703