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Involutivité des variétés microcaractéristiques. (Involutivity of microcharacteristic varieties). (French) Zbl 0619.35009

The purpose of this paper is to give a new proof of the involutivity of characteristic varieties of microdifferential systems. Let \({\mathfrak M}\) be a system of (mirco-) differential equations on a complex manifold X. As a fundamental result on \({\mathcal M}\), we know that the characteristic variety of \({\mathcal M}\) is an involutive subvariety in the cotangent bundle \(T^*X\). The authors of this paper give a new proof of this fact. They prove that the intersection of an involutive subset V of a complex analytic Poisson manifold (i.e., a manifold with the structure of Lie algebra of Poisson brackets) and the zeros of a holomorphic function f is also involutive if the associated Hamiltonian vector field is tangent to V, and they apply this result to give the new proof of involutivity.
Reviewer: M.Muro

MSC:

35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
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References:

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