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Finite groups of birational transformations
P. 413–437.
We survey new results on finite groups of birational transformations of algebraic varieties.
Publication based on the results of:
Arzhantsev I., Petravchuk A. P., Mathematical notes 2009 Vol. 86 No. 5 P. 625–628
Every subfield K(φ) of the field of rational fractions K(x_1, . . . , x_n) is contained in a unique maximal subfield of the form K(ψ). The element ψ is said to be generating for the element φ. A subfield of K(x_1, . . . , x_n) is said to be saturated if, together with ...
Added: June 13, 2025
Perepechko A., Mathematical notes 2021 Vol. 110 No. 5 P. 732–737
Affine algebraic surfaces of Markov type of the form (Formula presented.) are studied. Their automorphism groups are found. ...
Added: October 28, 2022
Prokhorov Y., / Series arXiv "math". 2021.
We survey new results on finite groups of birational transformations of algebraic varieties. ...
Added: November 25, 2021
Арутюнов А. А., Kosolapov L., Finite Fields and Their Applications 2021 Vol. 76 Article 101921
In this paper we establish decomposition theorems for derivations of group rings. We provide a topological technique for studying derivations of a group ring A[G] in case G has finite conjugacy classes. As a result, we describe all derivations of algebra A[G] for the case when G is a finite group, or G is an FC-group. In addition, we describe an algorithm to explicitly calculate all derivations of ...
Added: October 4, 2021
Shramov K., European Journal of Mathematics 2021 Vol. 7 P. 591–612
We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi–Brauer surfaces over fields of characteristic zero. ...
Added: September 8, 2021
Rumynin D., Taylor J., Linear Algebra and its Applications 2021 Vol. 610 P. 135–168
We use the structure of finite-dimensional graded algebras to develop the theory of antilinear representations of finite C_2-graded groups. A finite C_2-graded group is a finite group with a subgroup of index 2. In this theory the subgroup acts linearly, while the other coset acts antilinearly. We introduce antilinear blocks, whose structure is a crucial ...
Added: September 7, 2021
Shramov K., / Series arXiv "math". 2020.
We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi-Brauer surfaces over fields of characteristic zero. ...
Added: August 19, 2020
Shramov K., / Series arXiv "math". 2019.
We show that automorphism groups of Hopf and Kodaira surfaces have unbounded finite subgroups. For elliptic fibrations on Hopf, Kodaira, bielliptic, and K3 surfaces, we make some observations on finite groups acting along the fibers and on the base of such a fibration. ...
Added: November 19, 2019
Popov V. L., Doklady Mathematics 2018 Vol. 98 No. 2 P. 413–415
The compressibility of certain types of finite groups of birational automorphisms of algebraic varieties is established. ...
Added: November 13, 2018
Gavrilovich M., / Series arxiv "math.CT". 2017.
We illustrate the generative power of the lifting property (orthogonality of morphisms in a category) as means of defining natural elementary mathematical concepts by giving a number of examples in various categories, in particular showing that many standard elementary notions of abstract topology can be defined by applying the lifting property to simple morphisms of ...
Added: July 21, 2017
Expressing the statement of the Feit-Thompson theorem with diagrams in the category of finite groups
Gavrilovich M., / Series math.GR "arxiv". 2017.
We reformulate the statement of the Feit-Thompson theorem in terms of diagrams in the category of finite groups, namely iterations of the Quillen lifting property with respect to particular morphisms. ...
Added: July 20, 2017
Busjatskaja I., Monastyrsky M. I., , in: Symmetry: Art and Science. Special Issue for the Congress-Festival of ISIS-Symmetry.: Athens: The Hellenic Open University, 2013. P. 248–253.
The paper examines the significance of Platonic Solids in different parts of modern science. ...
Added: January 30, 2014
Athens: The Hellenic Open University, 2013.
The book contains the reports of the member of the congress from the different countres. They consider the idea of the symmety in the science and in the art. ...
Added: January 30, 2014