Compositions of birational endomorphisms of the affine plane

Abstract

Let A^2 denote the affine plane over an algebraically closed field of arbitrary characteristic. Besides contributing several new results in the general theory of birational endomorphisms of A^2, this article describes certain classes of birational endomorphisms f 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 A^2.

arXiv comment37 pages. Typos corrected, 3.16 improved, one reference added

References in corpus (1)

• Generally rational polynomials in two variables

Cited by in corpus (1)

• Field generators in two variables and birational endomorphisms of ${\mathbb{A}}^2$