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Monodromy and Connectedness
Author(s) -
Ran Z.
Publication year - 2000
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609300006962
Subject(s) - subvariety , mathematics , social connectedness , monodromy , irreducibility , pure mathematics , space (punctuation) , intersection (aeronautics) , geography , variety (cybernetics) , psychology , statistics , cartography , linguistics , philosophy , psychotherapist
The purpose of this note is initially to present an elementary but surprising connectedness principle pertaining to the intersection of a fixed subvariety X of some ambient space Z with another subvariety Y which is ‘mobile’ (in the sense of being movable, rather than actually moving). It is via this mobility that monodromy enters the picture, permitting the crucial passage from ‘relative’ or total‐space irreducibility to ‘absolute’ or fibrewise connectedness (and sometimes irreducibility). A general form of this principle is given in Theorem 2 below. 1991 Mathematics Subject Classification 14C99, 15N05.