Completely reducible hypersurfaces in a pencil
By J. V Pereira, Sergey Yuzvinsky. 2007
72 citations recorded by the source corpus.
Abstract We study completely reducible fibers of pencils of hypersurfaces on P n and associated codimension one foliations of 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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/dc07997c2b9e6d429a99a09a18512aa9bd852572
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Hyperplane arrangements and Milnor fibrations (2013, result): “The next theorem, which combines results of Pereira–Yuzvinsky [55] and Yuzvinsky [66], summarizes what is known about the existence of non-trivial multinets on arrangements.”
- Multinets, parallel connections, and Milnor fibrations of arrangements (2012, result): “ne multiplicity 1 and putting one hyperplane in each class. However, the existence of multinets for which |X| >1 is much more subtle. We distill some of the known results, as follows. Theorem 5.3 ([PY08], [Yu09]). Let (A 1,...,Ak) be a multinet on A, with multiplicity vector mand base locus X. MI”
- A new bound on the number of special fibers in a pencil of curves (2008, unknown): “hyperplane complements.”
- The Milnor fibration of a hyperplane arrangement: from modular resonance to algebraic monodromy (2014, background): “Works of Yuzvinsky [58, 59] and Pereira–Yuzvinsky [50] show that, if N is a k-multinet on a realizable matroid, with base locus of size greater than 1, then k = 3 or 4; furthermore, if N is not reduced, then k must equal 3.”