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Abstract: In this article, we define a non-commutative deformation of the -symplecticinvariants- of an algebraic hyperelliptical plane curve. The necessarycondition for our definition to make sense is a Bethe ansatz. The commutativelimit reduces to the symplectic invariants, i.e. algebraic geometry, and thuswe define non-commutative deformations of some algebraic geometry quantities.In particular our non-commutative Bergmann kernel satisfies a Rauch variationalformula. Those non-commutative invariants are inspired from the large Nexpansion of formal non-hermitian matrix models. Thus they are expected to berelated to the enumeration problem of discrete non-orientable surfaces ofarbitrary topologies.



Autor: Bertrand Eynard SPhT, Olivier Marchal SPhT, CRM

Fuente: https://arxiv.org/







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