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Rank one local systems and forms of degree one

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Title
Rank one local systems and forms of degree one
Author(s)
Budur N.; Wang B.; Youngho Yoon
Publication Date
2016
Journal
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, v.2016, no.13, pp.3849 - 3855
Publisher
OXFORD UNIV PRESS
Abstract
Cohomology support loci of rank one local systems of a smooth quasi-projective complex algebraic variety are finite unions of torsion-translated complex subtori of the character variety of the fundamental group. Tangent spaces of the character variety are (partially) represented by logarithmic 1-forms. In this paper, we give a relation between cohomology support loci and the natural strata of 1-forms given by the dimension of the vanishing locus. This relation generalizes the one for the projective case due to Green and Lazarsfeld and also generalizes the partial relation due to Dimca in the quasi-projective case. © The Author(s) 2015
URI
https://pr.ibs.re.kr/handle/8788114/2830
ISSN
1073-7928
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
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