Xavier Gómez-Mont: Grothendieck residue in the Jacobian algebra and cup product in vanishing...

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The Jacobian algebra, obtained from the ring of germs of functions modulo the partial derivatives of a function f with an isolated singularity, has a non-degenerate bilinear form, Grothendieck Residue, for which multiplication by f is a symmetric nilpotent operator. The vanishing cohomology of the Milnor Fibre has a bilinear form induced by cup product for which the nilpotent operator N, the logarithm of the unipotent part of the monodromy, is antisymmetric. Using the nilpotent operators we obtain primitive parts of the bilinear form and we compare both bilinear forms. In particular, over R, we obtain signatures of these primitive forms, that we compare.

Recording during the thematic meeting: « Local and Global Invariants of Singularities» the February 24, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France)

Film maker: Guillaume Hennenfent