IJPAM: Volume 20, No. 2 (2005)

CURVILINEAR JOINS AND CURVILINEAR
SECANT VARIETIES TO SUBVARIETIES
OF A PROJECTIVE SPACE

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Fix integral subvarieties $X_1,\dots X_s$ of ${\bf {P}}^n$ and integers $m_i>0$, $1 \le i \le s$. Here we introduce and study the variety $\mathcal {C} (X_1,m_1,\dots ,X_s$,
$m_s) \subseteq {\bf {P}}^n$ defined as the closure in ${\bf {P}}^n$ of the union of all linear subspaces $\langle Z_1\cup \cdots \cup Z_s\rangle$, where $Z_i$ is a length $m_i$ connected curvilinear subscheme of $X_i$.

Received: March 15, 2005

AMS Subject Classification: 14N05

Key Words and Phrases: osculating spaces, secant variety, tangential variety, join of projective varieties, curvilinear zero-dimensional scheme

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 20
Issue: 2