The Experts below are selected from a list of 34020 Experts worldwide ranked by ideXlab platform
Keiji Oguiso - One of the best experts on this subject based on the ideXlab platform.
-
a surface in odd characteristic with discrete and non finitely generated Automorphism Group
Advances in Mathematics, 2020Co-Authors: Keiji OguisoAbstract:Abstract It was proved by Tien-Cuong Dinh and me that there is a smooth complex projective surface whose Automorphism Group is discrete and not finitely generated. In this paper, after observing finite generation of the Automorphism Group of any smooth projective surface birational to any K3 surface over any algebraic closure of the prime field of odd characteristic, we will show that there is a smooth projective surface, birational to some K3 surface, such that the Automorphism Group is discrete and not finitely generated, over any algebraically closed field of odd characteristic of positive transcendental degree over the prime field.
-
a surface in odd characteristic with discrete and non finitely generated Automorphism Group
arXiv: Algebraic Geometry, 2019Co-Authors: Keiji OguisoAbstract:It was proved by Tien-Cuong Dinh and me that there is a smooth complex projective surface whose Automorphism Group is discrete and not finitely generated. In this paper, we will show that there is a smooth projective surface, birational to some K3 surface, such that the Automorphism Group is discrete and not finitely generated, over any algebraically closed field of odd characteristic except precisely an algebraic closure of the prime field.
-
a surface with discrete and non finitely generated Automorphism Group
arXiv: Algebraic Geometry, 2017Co-Authors: Tiencuong Dinh, Keiji OguisoAbstract:We show that there is a smooth complex projective variety, of any dimension greater than or equal to two, whose Automorphism Group is discrete and not finitely generated. Moreover, this variety admits infinitely many real forms which are mutually non-isomorphic over the real number field. Our result is inspired by the work of Lesieutre and answers questions by Dolgachev, Esnault and Lesieutre.
Andrew Zimmer - One of the best experts on this subject based on the ideXlab platform.
-
the Automorphism Group and limit set of a bounded domain ii the convex case
arXiv: Complex Variables, 2017Co-Authors: Andrew ZimmerAbstract:For convex domains with $C^{1,\epsilon}$ boundary we give a precise description of the Automorphism Group: if an orbit of the Automorphism Group accumulates on at least two different closed complex faces of the boundary, then the Automorphism Group has finitely many components and the connected component of the identity is the almost direct product of a compact Group and a non-compact connected simple Lie Group with real rank one and finite center. In this case, we also show the limit set is homeomorphic to a sphere and prove a gap theorem: either the domain is biholomorphic to the unit ball (and the limit set is the entire boundary) or the limit set has co-dimension at least two in the boundary.
-
characterizing domains by the limit set of their Automorphism Group
Advances in Mathematics, 2017Co-Authors: Andrew ZimmerAbstract:Abstract In this paper we study the Automorphism Group of smoothly bounded convex domains. We show that such a domain is biholomorphic to a “polynomial ellipsoid” (that is, a domain defined by a weighted homogeneous balanced polynomial) if and only if the limit set of the Automorphism Group intersects at least two closed complex faces of the set. The proof relies on a detailed study of the geometry of the Kobayashi metric and ideas from the theory of non-positively curved metric spaces. We also obtain a number of other results including the Greene–Krantz conjecture in the case of uniform non-tangential convergence, new results about continuous extensions (of biholomorphisms and complex geodesics), and a new Wolff–Denjoy theorem.
-
characterizing the unit ball by its projective Automorphism Group
arXiv: Differential Geometry, 2015Co-Authors: Andrew ZimmerAbstract:In this paper we study the projective Automorphism Group of domains in real, complex, and quaternionic projective space and present two new characterizations of the unit ball in terms of the size of the Automorphism Group and the regularity of the boundary.
-
Characterizing polynomial domains by their Automorphism Group
arXiv: Complex Variables, 2015Co-Authors: Andrew ZimmerAbstract:In this paper we study the Automorphism Group of bounded convex domains with smooth boundary. In particular, we show that such a domain is biholomorphic to a weighted homogeneous polynomial domain if and only if the limit set of the Automorphism Group intersects at least two closed complex faces of the set. The proof combines rescaling arguments with a detailed study of the geometry of the Kobayashi metric. In particular a number of ideas from the theory of non-positively curved metric spaces are used. A key step in the argument is establishing the Greene-Krantz conjecture in the case of uniform non-tangential convergence. We also obtain new results about the behavior of holomorphic maps between convex domains, in particular new results about continuous extensions (of bi-holomorphisms and complex geodesics) and a new Denjoy-Wolff theorem.
Li Yang - One of the best experts on this subject based on the ideXlab platform.
-
The Automorphism Group of the Lie Ring of Real Skew-Symmetric Matrices
Abstract and Applied Analysis, 2013Co-Authors: Jinli Xu, Baodong Zheng, Li YangAbstract:Denote by the set of all skew-symmetric matrices over the field of real numbers, which forms a Lie ring under the usual matrix addition and the Lie multiplication as , . In this paper, we characterize the Automorphism Group of the Lie ring .
Nicholas Young - One of the best experts on this subject based on the ideXlab platform.
-
The Automorphism Group of the tetrablock
Journal of the London Mathematical Society, 2008Co-Authors: Nicholas YoungAbstract:The tetrablock is shown to be inhomogeneous and its Automorphism Group is determined. A type of Schwarz lemma for the tetrablock is proved. The action of the Automorphism Group is described in terms of a certain natural foliation by complex geodesic discs.
Bryna Kra - One of the best experts on this subject based on the ideXlab platform.
-
The stabilized Automorphism Group of a subshift
arXiv: Dynamical Systems, 2020Co-Authors: Yair Hartman, Bryna Kra, Scott SchmiedingAbstract:For a mixing shift of finite type, the associated Automorphism Group has a rich algebraic structure, and yet we have few criteria to distinguish when two such Groups are isomorphic. We introduce a stabilization of the Automorphism Group, study its algebraic properties, and use them to distinguish many of the stabilized Automorphism Groups. We also show that for a full shift, the subGroup of the stabilized Automorphism Group generated by elements of finite order is simple, and that the stabilized Automorphism Group is an extension of a free abelian Group of finite rank by this simple Group.
-
distortion and the Automorphism Group of a shift
Journal of Modern Dynamics, 2018Co-Authors: Van Cyr, Bryna Kra, John Franks, Samuel PetiteAbstract:The set of Automorphisms of a one-dimensional subshift \begin{document} $(X, σ)$ \end{document} forms a countable, but often very complicated, Group. For zero entropy shifts, it has recently been shown that the Automorphism Group is more tame. We provide the first examples of countable Groups that cannot embed into the Automorphism Group of any zero entropy subshift. In particular, we show that the Baumslag-Solitar Groups \begin{document} ${\rm BS}(1,n)$ \end{document} and all other Groups that contain exponentially distorted elements cannot embed into \begin{document} ${\rm Aut}(X)$ \end{document} when \begin{document} $h_{{\rm top}}(X) = 0$ \end{document} . We further show that distortion in nilpotent Groups gives a nontrivial obstruction to embedding such a Group in any low complexity shift.
-
distortion and the Automorphism Group of a shift
arXiv: Dynamical Systems, 2016Co-Authors: Van Cyr, Bryna Kra, John Franks, Samuel PetiteAbstract:The set of Automorphisms of a one-dimensional \shift $(X, \sigma)$ forms a countable, but often very complicated, Group. For zero entropy shifts, it has recently been shown that the Automorphism Group is more tame. We provide the first examples of countable Groups that cannot embed into the Automorphism Group of any zero entropy \shiftno. In particular, we show that the Baumslag-Solitar Groups ${\rm BS}(1,n)$ and all other Groups that contain exponentially distorted elements cannot embed into ${\rm Aut}(X)$ when $h_{\rm top}(X)=0$. We further show that distortion in nilpotent Groups gives a nontrivial obstruction to embedding such a Group in any low complexity shift.
-
the Automorphism Group of a minimal shift of stretched exponential growth
Journal of Modern Dynamics, 2016Co-Authors: Van Cyr, Bryna KraAbstract:The Group of Automorphisms of a symbolic dynamical system is countable, but often very large. For example, for a mixing subshift of finite type, the Automorphism Group contains isomorphic copies of the free Group on two generators and the direct sum of countably many copies of $\mathbb{Z}$. In contrast, the Group of Automorphisms of a symbolic system of zero entropy seems to be highly constrained. Our main result is that the Automorphism Group of any minimal subshift of stretched exponential growth with exponent $<1/2$, is amenable (as a countable discrete Group). For shifts of polynomial growth, we further show that any finitely generated, torsion free subGroup of Aut(X) is virtually nilpotent.
-
The Automorphism Group of a shift of linear growth: beyond transitivity
arXiv: Dynamical Systems, 2014Co-Authors: Van Cyr, Bryna KraAbstract:For a finite alphabet $\mathcal{A}$ and shift $X\subseteq\mathcal{A}^{\mathbb{Z}}$ whose factor complexity function grows at most linearly, we study the algebraic properties of the Automorphism Group ${\rm Aut}(X)$. For such systems, we show that every finitely generated subGroup of ${\rm Aut}(X)$ is virtually ${\mathbb Z}^d$, in contrast to the behavior when the complexity function grows more quickly. With additional dynamical assumptions we show more: if $X$ is transitive, then ${\rm Aut}(X)$ is virtually $\mathbb Z$; if $X$ has dense aperiodic points, then ${\rm Aut}(X)$ is virtually ${\mathbb Z}^d$. We also classify all finite Groups that arise as the Automorphism Group of a shift.
