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Mathematics > Algebraic Geometry
Title: The symplectic form associated to a singular Poisson algebra
(Submitted on 22 Mar 2024)
Abstract: Given an affine Poisson algebra, that is singular one may ask whether there is an associated symplectic form. In the smooth case the answer is obvious: for the symplectic form to exist the Poisson tensor has to be invertible. In the singular case, however, derivations do not form a projective module and it is less clear what non-degenerate means. For a symplectic singularity one may naively ask if there is indeed an analogue of a symplectic form. We examine an example of a symplectic singularity, namely the double cone, and show that here such a symplectic form exists. We use the naive de Rham complex of a Lie-Rinehart algebra. Our analysis of the double cone relies on Gr\"obner bases calculations.
Submission history
From: Hans-Christian Herbig [view email][v1] Fri, 22 Mar 2024 02:48:16 GMT (256kb,D)
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