IJPAM: Volume 12, No. 1 (2004)

MONODROMY GROUPS AND A THEOREM OF
BERTINI FOR COMPLEX BANACH
ANALYTIC PROJECTIVE SETS

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


Abstract.Here we prove the following result. Let $V$ be a complex Banach space and $X \subset {\bf {P}}(V)$ a closed finitely determined irreducible subset with codimension $m>0$. Fix any integer $y>m$. Then for a sufficiently general $A\in G(y+1,V)$ the closed analytic subset $(X\cap A)_{red}$ is an irreducible projective variety of dimension $y-m$ and the scheme $X\cap A$ is reduced at a general point of $(X\cap A)_{red}$.

Received: February 5, 2003

AMS Subject Classification: 32K05, 14N05

Key Words and Phrases: complex Banach manifold, infinite-dimensional projective space, monodromy group, Bertini Theorem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 12
Issue: 1