Critical set of the master function and characteristic variety of the associated Gauss-Manin differential equations

DOI10.1007/s40598-015-0020-8zbMath1323.32024arXiv1410.2438OpenAlexW2963475837MaRDI QIDQ500660

Alexander Varchenko

Publication date: 5 October 2015

Published in: Arnold Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.2438

zbMATH Keywords

characteristic varietycomplex partial differential equationsGauss-Manin differential equationsmaster functions

Mathematics Subject Classification ID

Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60) Monodromy; relations with differential equations and (D)-modules (complex-analytic aspects) (32S40) Other partial differential equations of complex analysis in several variables (32W50)

Related Items

POTENTIALS OF A FROBENIUS-LIKE STRUCTURE

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• KZ characteristic variety as the zero set of classical Calogero-Moser Hamiltonians
• Characteristic variety of the Gauss-Manin differential equations of a generic parallelly translated arrangement
• Quantum integrable model of an arrangement of hyperplanes
• The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz
• Stratified Morse theory in arrangements
• The equivariant Orlik-Solomon algebra
• Arrangements of hyperplanes and Lie algebra homology
• Discriminantal arrangements, fiber polytopes and formality
• The number of critical points of a product of powers of linear functions
• Quantum cohomology of flag manifolds and Toda lattices
• Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors
• Arrangements and Frobenius like structures
• Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety
• Bethe algebra of the gl_{N+1} Gaudin model and algebra of functions on the critical set of the master function
• Schubert calculus and representations of the general linear group
• Stationary Phase Integrals, Quantum Toda Lattices, Flag Manifolds and the Mirror Conjecture
• Cohomology of the brieskorn-orlik-solomon algebras
• The contravariant form on singular vectors of a projective arrangement
• A higher invariant for matroids
• Norm of a Bethe vector and the Hessian of the master function
• Frontiers of reality in Schubert calculus
• Arrangements and hypergeometric integrals
• On a conjecture of Varchenko