IJPAM: Volume 13, No. 4 (2004)

PROJECTIVE VARIETIES AND SETS OF
OSCULATING SPACES IN UNIFORM POSITION

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


Abstract.Let $X\subset {\bf {P}}^r$ be an integral projective variety. For every $P\in X_{reg}$ and $m>0$ let $O(X,mP)$ be the osculating space of $X$. Here we give the set-up to show that in several cases there must be $k$-ples of distinct points $(P_1,\dots ,P_k), (Q_1,\dots ,Q_k)\in X_{reg}^k$ such that $\mbox{\rm dim}(\langle O(X,mP_1)\cup
\cdots \cup O(X,mP_k)\rangle ) \ne \mbox{\rm dim}(\langle O(X,mQ_1)\cup \cdots \cup O(X,mQ_k)\rangle )$.

Received: March 7, 2004

AMS Subject Classification: 14N05

Key Words and Phrases: osculating linear space, uniform position principle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 13
Issue: 4