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Preprint Number 77

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77. Boris Zilber
Non-commutative Zariski geometries and their classical limit

Submission date: 11 July 2007


We undertake a case study of two series of nonclassical Zariski geometries. We show that these geometries can be realised as representations of certain noncommutative $C^*$-algebras and introduce a natural limit construction which for each of the two series produces a classical U(1)-gauge field over a 2-dimensional Riemann surface.

Mathematics Subject Classification: 81D07, 81R60

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