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Degree growth of polynomial automorphisms and birational maps: some examples

Authors
  • Déserti, Julie1
  • 1 Sorbonne Universités, UPMC Univ Paris 06, Université Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, CNRS, Paris, 75013, France , Paris (France)
Type
Published Article
Journal
European Journal of Mathematics
Publisher
Springer International Publishing
Publication Date
Aug 21, 2017
Volume
4
Issue
1
Pages
200–211
Identifiers
DOI: 10.1007/s40879-017-0175-z
Source
Springer Nature
Keywords
License
Yellow

Abstract

We give examples of new degree growths for polynomial automorphisms of Ck\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}^k$$\end{document} and birational maps of . Namely, if k is an integer ⩾3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\geqslant 3$$\end{document}, then for any we provide polynomial automorphisms f of Ck\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}^k$$\end{document} such that , and for all 0⩽ℓ⩽k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0\leqslant \ell \leqslant k$$\end{document} we provide birational maps ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi $$\end{document} of such that .

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