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Bulletin of the London Mathematical Society Advance Access originally published online on December 11, 2007
Bulletin of the London Mathematical Society 2007 39(6):949-961; doi:10.1112/blms/bdm098
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© 2007 London Mathematical Society

Tangential projections and secant defective varieties

Roberto Muñoz

Departamento de Matemática Aplicada
Universidad Rey Juan Carlos
28933 Móstoles (Madrid)
Spain
roberto.munoz@urjc.es

José Carlos Sierra

Departamento de Álgebra
Facultad de Matemáticas
Universidad Complutense de Madrid
Ciudad Universitaria
28040 Madrid
Spain
jcsierra@mat.ucm.es

Luis E. Solá Conde

Departamento de Matemática Aplicada
Universidad Rey Juan Carlos
28933 Móstoles (Madrid)
Spain

Received 20 February 2007. Revision received 22 June 2007.

Going one step further in Zak's classification of Scorza varieties with secant defect equal to one, we characterize the Veronese embedding of Pn given by the complete linear system of quadrics and its smooth projections from a point, as the only smooth irreducible complex and non-degenerate projective subvarieties of PN that can be projected isomorphically into P2n when Formula

This research has been partially supported by the project MTM2006-04785 of the Spanish Government.

2000 Mathematics Subject Classification 14N05 (primary), 14M07 (secondary).


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