IJPAM: Volume 66, No. 4 (2011)

ON THE REAL PART OF SECANT VARIETIES
OF REAL VARIETIES EMBEDDED IN
A PROJECTIVE SPACE

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $X\subset \mathbb {P}^n$ a smooth variety defined over $\mathbb {R}$. Here we describe a large part of the real part of the secant varieties $\sigma _k(X)\subsetneq \mathbb {P}^n$ in term of the connected components of $X(\mathbb {R})$ and $X(\mathbb {C})\setminus X(\mathbb {R})$ when $X$ is not weakly $(k-1)$-defective.

Received: August 2, 2010

AMS Subject Classification: 14N05

Key Words and Phrases: $X$-rank, real projective variety secant variety

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 4