Completely reducible hypersurfaces in a pencil

Details Completely reducible hypersurfaces in a pencil Completely reducible hypersurfaces in a pencil

2007-01-10

arxiv.org/abs/math/0701312v2

Advances in Mathematics 219 (2008), no. 2, 672--688.

Mathematics

Algebraic Geometry

15 pages, 2 figures

Scientific paper

10.1016/j.aim.2008.05.014

We study completely reducible fibers of pencils of hypersurfaces on $\mathbb P^n$ and associated codimension one foliations of $\mathbb P^n$. Using methods from theory of foliations we obtain certain upper bounds for the number of these fibers as functions only of $n$. Equivalently this gives upper bounds for the dimensions of resonance varieties of hyperplane arrangements. We obtain similar bounds for the dimensions of the characteristic varieties of the arrangement complements.

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