Displaying similar documents to “Local reduction theorems and invariants for singular contact structures”

The index of a vector field tangent to a hypersurface and the signature of the relative jacobian determinant

Xavier Gómez-Mont, Pavao Mardešić (1997)

Annales de l'institut Fourier

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Given a real analytic vector field tangent to a hypersurface V with an algebraically isolated singularity we introduce a relative Jacobian determinant in the finite dimensional algebra B Ann B ( h ) associated with the singularity of the vector field on V . We show that the relative Jacobian generates a 1-dimensional non-zero minimal ideal. With its help we introduce a non-degenerate bilinear pairing, and its signature measures the size of this point with sign. The signature satisfies a law of conservation...

On the Jung method in positive characteristic

Olivier Piltant (2003)

Annales de l’institut Fourier

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Let X ¯ be a germ of normal surface with local ring R ¯ covering a germ of regular surface X with local ring R of characteristic p > 0 . Given an extension of valuation rings W / V birationally dominating R ¯ / R , we study the existence of a new such pair of local rings R ¯ ' / R ' birationally dominating R ¯ / R , such that R ' is regular and R ¯ ' has only toric singularities. This is achieved when W / V is defectless or when [ W : V ] is equal to p