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Summary: COHOMOLOGY SUPPORT LOCI FOR LOCAL SYSTEMS AND
HIGGS BUNDLES
DONU ARAPURA
U. Michigan, May 2009
X will stand for a smooth projective variety over C throughout these notes. To
simplify some statements, it will be convenient (but not essential) to also assume
that
(*) H2
(X, Z) is torsion free.
To fix notation recall: The Picard variety Pic0
(X) is the set of line bundles
with trivial first Chern class (the Chern class can be taken H2
(X, C), since we are
assuming that H2
(X, Z) is torsion free) This is an abelian variety of dimension
q(X) = dim H1
(X, OX). Green and Lazarsfeld have introduced the cohomology
support loci
Si
(X) = {L Pic0
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