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Summary: ESSENTIAL COORDINATE COMPONENTS OF
CHARACTERISTIC VARIETIES
ENRIQUE ARTAL BARTOLO
, JORGE CARMONA RUBER
, AND JOS´E
IGNACIO COGOLLUDO AGUST´IN
Abstract. In this note we give an algebraic and topological in-
terpretation of essential coordinate components of characteristic
varieties and illustrate their importance in an example.
1. Introduction
Let C = C0 C1 · · · Cr be a projective algebraic curve in P2
. For
convenience, we assume C0 to be a line intersecting the curve C :=
C1 · · · Cr transversally. In this context, C 2
will refer to P2
\ C0. Let
X := P2
\C denote its complement and ~X the universal abelian cover of
X. The group of covering transformations of ~X X acts on H1( ~X; Z)
and endows it with a Z[H1(X; Z)]-module structure. Tensoring by C
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