The characteristic variety of a generic foliation. (English) Zbl 1296.37040
Author’s abstract: “We confirm a conjecture of J. Bernstein and V. Lunts [Invent. Math. 94, No. 2, 223–243 (1988; Zbl 0658.32009)] which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.”
In this paper, the author studies the invariant subvarieties in the characteristic variety of a one-dimensional holomorphic foliation \(\mathcal{F}\) invariant by its first prolongation. This problem is connected to the classification of irreducible modules over the Weyl algebras which was treated by Bernstein-Lunts.
In this paper, the author studies the invariant subvarieties in the characteristic variety of a one-dimensional holomorphic foliation \(\mathcal{F}\) invariant by its first prolongation. This problem is connected to the classification of irreducible modules over the Weyl algebras which was treated by Bernstein-Lunts.
Reviewer: Isaia Nisoli (Rio de Janeiro)
MSC:
| 37F75 | Dynamical aspects of holomorphic foliations and vector fields |
| 16S32 | Rings of differential operators (associative algebraic aspects) |
| 37J30 | Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) |
| 32C38 | Sheaves of differential operators and their modules, \(D\)-modules |
Citations:
Zbl 0658.32009References:
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