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arXiv · 1810.09094

Degree growth for tame automorphisms of an affine quadric threefold

Nguyen-Bac Dang
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Abstract

In this paper, we consider the degree sequences of the tame automorphisms preserving an affine quadric threefold. Using some valuatives estimates derived from the work of Shestakov-Umirbaev and the action of this group on a CAT(0), Gromov-hyperbolic square complex constructed by Bisi-Furter-Lamy, we prove that the dynamical degrees of tame elements avoid any value strictly between 1 and 4/3. As an application, these methods allow us to characterize when the growth exponent of the degree of a random product of finitely many tame automorphisms is positive.

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BibTeXRIS

Nguyen-Bac Dang. 2018-10-22. Degree growth for tame automorphisms of an affine quadric threefold. https://doi.org/10.2140/ant.2024.18.1

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