Journal of Noncommutative Geometry
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Published online: 2016-03-22
Noncommutative versions of some classical birational transformationsDennis Presotto and Michel Van den Bergh (1) Hasselt University, Belgium
(2) Hasselt University, Belgium
In this paper we generalize some classical birational transformations to the noncommutative case. In particular we show that 3-dimensional quadratic Sklyanin algebras (noncommutative projective planes) and 3-dimensional cubic Sklyanin algebras (non-commutative quadrics) have the same function field. In the same veinwe construct an analogue of the Cremona transform for non-commutative projective planes.
Keywords: Birational transformation, Cremona transform, Sklyanin algebras, non-commutative surfaces
Presotto Dennis, Van den Bergh Michel: Noncommutative versions of some classical birational transformations. J. Noncommut. Geom. 10 (2016), 221-244. doi: 10.4171/JNCG/232