IJPAM: Volume 37, No. 1 (2007)

THE MONODROMY GROUP OF THE HYPERPLANE
SECTION OF THE JOIN OF $d$ GENERIC
POINTS IN 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 a hyperplane $H \subset {\bf {P}}^n$. For all general $(P_1,\dots ,P_d)\in ({\bf {P}}^n)^d$ let $X_d$ be the union of all lines $\langle \{P_i,P_j\}\rangle$, $1 \le i < j \le d$. Hence $X_d\cap H$ is the union of $\binom{d}{2}$ points. Moving the points $P_1,\dots ,P_d$ we get a permutation group $G_{d,n}$ on $\{1,\dots ,\binom{d}{2}\}$: the Galois (or monodromy) group of the join of $d$ generic points of ${\bf {P}}^n$. We study this primitive (but not $2$-transitive) permutation group.

Received: February 27, 2007

AMS Subject Classification: 14N05

Key Words and Phrases: monodromy group, generic Galois group, hyperplane section, secant variety

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 37
Issue: 1