Construction of an AS-regular sub-$\mathbb{Z}$-algebra of the 2-veronese of an AS-regular algebra

Michel Van den Bergh, Dennis Presotto

Published 2014-10-20Version 1

In this paper we generalize some classical birational transformations to the non-commutative case. In particular we show that 3-dimensional quadratic Sklyanin algebras (non-commutative projective planes) and 3-dimensional cubic Sklyanin algebras (non-commutative quadrics) have the same function field. In the same vein we construct and analogue of the Cremona transform for non-commutative projective planes.