Vanishing cycles in complex symplectic geometry

Details Vanishing cycles in complex symplectic geometry Vanishing cycles in complex symplectic geometry

2005-11-22

arxiv.org/abs/math/0511555v2

Mathematics

Algebraic Geometry

18 pages

Scientific paper

We study the vanishing cycles on the Milnor fibre of a holomorphic map germ with special kind of non-isolated singularities which appear in symplectic geometry. We show, under assumptions given in the text, that the Lefschetz vanishing cycles freely generate the corresponding homology group of the Milnor fibre. We study two examples of applications: involutive systems in symplectic geometry (as characteristic varieties of $\hbar$-differential equations are of this type) and ajoint orbits in Lie algebras.

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