Kraft, Hanspeter Zaidenberg, M

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...

Espinoza, Bastián Maass, Alejandro

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...

Perepechko, A. Yu.
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...

Izquierdo, Milagros Jones, Gareth A. Reyes-Carocca, Sebastián

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...

Shramov, K. A.
Published in
Mathematical Notes

Kuznetsova, A. A.
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 ...

Nikulin, Viacheslav V.
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...

Kikyo, Hirotaka

The automorphism groups of Hrushovski's pseudoplanes associated to rational numbers α with 1/3 >α≥1/4 are simple groups.

Avilov, A. A.
Published in
Mathematical Notes

The forms of the Segre cubic over non-algebraically closed fields, their automorphisms groups, and equivariant birational rigidity are studied. In particular, it is shown that all forms of the Segre cubic over any field have a point and are cubic hypersurfaces.

Li, Zihao

The Kawamata-Morrison cone conjecture have attracted a lot of attention in algebraic geometry. In this thesis, the author will deal with this conjecture for Calabi-Yau 3-folds whose nef cone is polyhedral in chapter 3. In chapter 4, we will investigate the null cone and the automorphism group of Calabi-Yau 3-folds of Picard number $4$, which serves...