Quantum deformations of projective three-space

Brent Pym (University of Oxford)

Wednesday 4th February, 2015 16:00-17:00 Maths 516


In noncommutative projective geometry, quantum versions of projective space are often described in terms of their homogeneous coordinate rings, which are noncommutative analogues of polynomial rings.  The algebras corresponding to quantum projective planes were classified in geometric terms by Artin, Tate and Van den Bergh in a celebrated 1990 paper.  The related problem for projective three-space has received considerable attention, but the full classification remains elusive.  I will describe some recent progress on this problem, in which deformation quantization is combined with Cerveau and Lins Neto's classification of foliations on projective space to give a classification of the flat deformations of the polynomial ring in four variables as a graded Calabi--Yau algebra.

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