Multinets, parallel connections, and Milnor fibrations of arrangements
By Graham C. Denham, Alexander I. Suciu. 2012
49 citations recorded by the source corpus.
The characteristic varieties of a space are the jump loci for homology of rank 1 local systems. The way in which the geometry of these varieties may vary with the characteristic of the ground field is reflected in the homology of finite cyclic covers. We exploit this phenomenon to detect torsion in the homology of Milnor fibers of projective hypersurfaces. One tool we use is the interpretation of the degree 1 characteristic varieties of a hyperplane arrangement complement in terms of orbifold fibrations and multinets on the corresponding matroid. Another tool is a polarization construction, based on the parallel connection operad for matroids. Our main result gives a combinatorial machine for producing arrangements whose Milnor fibers have torsion in homology. In particular, this shows that Milnor fibers of hyperplane arrangements do not necessarily have a minimal cell structure.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/bf878e33cdbbe0e24833c07e7ad713c796e59158
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
Citations in the corpus
- Hyperplane arrangements and Milnor fibrations (2013, unknown): “49”
- The Milnor fibration of a hyperplane arrangement: from modular resonance to algebraic monodromy (2014, background): “On the combinatorial side, multinets and their relationship with complex resonance varieties, established in [27, 43] and further developed in [50, 59] play an important role in [12, 18, 20, 52, 53], and are key to our approach.”