The automorphism group Aut(X) of an affine variety X is an ind-group. Its Lie algebra is canonically embedded into the Lie algebra Vec(X) of vector fields on X. We study the relations between closed subgroups G of Aut(X) and the corresponding Lie subalgebras of Vec(X).We show that a subgroup G ⊆ Aut(X) generated by a family of connected algebraic s...
The automorphism group Aut(X) of an affine variety X is an ind-group. Its Lie algebra is canonically embedded into the Lie algebra Vec(X) of vector fields on X. We study the relations between closed subgroups G of Aut(X) and the corresponding Lie subalgebras of Vec(X).We show that a subgroup G ⊆ Aut(X) generated by a family of connected algebraic s...
It has been recently proved that the automorphism group of a minimal subshift with non-superlinear word complexity is virtually $\mathbb{Z}$ [DDPM15, CK15]. In this article we extend this result to a broader class proving that the automorphism group of a minimal S-adic subshift of finite alphabet rank is virtually $\mathbb{Z}$. The proof is based o...
We study the size of the automorphism group of two different types of random trees: Galton-Watson trees and Pólya trees. In both cases, we prove that it asymptotically follows a log-normal distribution. While the proof for Galton-Watson trees mainly relies on probabilistic arguments and a general result on additive tree functionals, generating func...
Published in Mathematical Notes
Abstract Affine algebraic surfaces of Markov type of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^2+y^2+z^2-xyz=c$$\end{document} are studied. Their autom...
We classify compact Riemann surfaces of genus g, where g−1 is a prime p, which have a group of automorphisms of order ρ(g−1)for some integer ρ≥1, and determine isogeny decompositions of the corresponding Jacobian varieties. This extends results of Belolipetzky and the second author for ρ>6, and of the first and third authors for ρ= 3, 4, 5 and 6. A...
Published in Mathematical Notes
Published in Mathematical Notes
Abstract We consider 3-subgroups in groups of birational automorphisms of rationally connected threefolds and show that any 3-subgroup can be generated by at most five elements. Moreover, we study groups of regular automorphisms of terminal Fano threefolds and prove that, in all cases which are not among several explicitly described exceptions any ...
Published in Mathematical Notes
Abstract We give more detail to our examples in [1] of K3 surfaces over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb C$$\end{document} which have an infinite...
The automorphism groups of Hrushovski's pseudoplanes associated to rational numbers α with 1/3 >α≥1/4 are simple groups.
