Noncommutative versions of some classical birational transformations

  • Dennis Presotto

    Hasselt University, Belgium
  • Michel Van den Bergh

    Hasselt University, Belgium

Abstract

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.

Cite this article

Dennis Presotto, Michel Van den Bergh, Noncommutative versions of some classical birational transformations. J. Noncommut. Geom. 10 (2016), no. 1, pp. 221–244

DOI 10.4171/JNCG/232