Compositions of birational endomorphisms of the affine plane

Pierrette Cassou-Noguès and Daniel Daigle

Vol. 272 (2014), No. 2, 353–394

DOI: 10.2140/pjm.2014.272.353

Abstract

Besides contributing several new results in the general theory of birational endomorphisms of ${\mathbb{A}}^2$, this article describes certain classes of birational endomorphisms $f:{\mathbb{A}}^2\to {\mathbb{A}}^2$ defined by requiring that the missing curves or contracting curves of $f$ are lines. The last part of the article is concerned with the monoid structure of the set of birational endomorphisms of ${\mathbb{A}}^2$.

Keywords

affine plane, birational morphism, plane curve

Mathematical Subject Classification 2010

Primary: 14R10, 14H50

Milestones

Received: 17 July 2013

Accepted: 7 November 2013

Published: 28 November 2014