Journal of Noncommutative Geometry

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Volume 10, Issue 1, 2016, pp. 221–244
DOI: 10.4171/JNCG/232

Published online: 2016-03-22

Noncommutative versions of some classical birational transformations

Dennis Presotto[1] and Michel Van den Bergh[2]

(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