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- Title
Resonance Varieties over Fields of Positive Characteristic.
- Authors
Falk, Michael J.
- Abstract
Let ?? be a hyperplane arrangement, and ?? a field of arbitrary characteristic. We show that the projective degree-one resonance variety ℛ1(??, ??) of ?? over ?? is ruled by lines, and identify the underlying algebraic line complex L(??, ??) in the Grassmannian ??(2, ??n), n=|??|. L(??, ??) is a union of linear line complexes corresponding to the neighborly partitions of subarrangements of ??. Each linear line complex is the intersection of a family of special Schubert varieties corresponding to a subspace arrangement determined by the partition.
- Subjects
VARIETIES (Universal algebra); ALGEBRA; GRASSMANN manifolds; MATHEMATICAL complexes; SCHUBERT varieties
- Publication
IMRN: International Mathematics Research Notices, 2007, Vol 2007, p1
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnm009