Pencils of plane curves and characteristic varieties

Details Pencils of plane curves and characteristic varieties Pencils of plane curves and characteristic varieties

2006-06-19

arxiv.org/abs/math/0606442v3

Mathematics

Algebraic Geometry

New results: First Prop. 3.18, Cor. 3.21 and Prop. 6.7 saying that all the possible translates actually do occur as components

Scientific paper

We give a geometric approach to the relation between the irreducible components of the characteristic varieties of local systems on a plane curve arrangement complement and the associated pencils of plane curves discovered recently by M. Falk and S. Yuzvinsky in the case of line arrangements, see mathAG/0603166. In this case, this geometric point of view was already hinted to by A. Libgober and S. Yuzvinsky. Our study yields new geometric insight on the translated components of the characteristic varieties, relating them to the multiplicities of curves in the associated pencil, in close analogy to the compact situation treated by A. Beauville.

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