scholarly journals Classification of Enriques surfaces with finite automorphism group in characteristic 2

2020 ◽  
pp. 390-459
Author(s):  
Shigeyuki Kondo
Keyword(s):  
Automorphism Group ◽  
Enriques Surfaces ◽  
Characteristic 2

scholarly journals Algebraic Surfaces of General Type with Small c21 in Positive Characteristic

2008 ◽  
Vol 191 ◽  
pp. 111-134 ◽  
Author(s):  
Christian Liedtke
Keyword(s):  
Characteristic Zero ◽  
General Type ◽  
Positive Characteristic ◽  
Algebraic Surfaces ◽  
Surfaces Of General Type ◽  
Arbitrary Characteristic ◽  
Numerical Invariants ◽  
Characteristic 2

AbstractWe establish Noether’s inequality for surfaces of general type in positive characteristic. Then we extend Enriques’ and Horikawa’s classification of surfaces on the Noether line, the so-called Horikawa surfaces. We construct examples for all possible numerical invariants and in arbitrary characteristic, where we need foliations and deformation techniques to handle characteristic 2. Finally, we show that Horikawa surfaces lift to characteristic zero.

scholarly journals On the classification of 3-dimensionalSL2(ℂ)-varieties

2000 ◽  
Vol 157 ◽  
pp. 129-147 ◽  
Author(s):  
Stefan Kebekus
Keyword(s):  
Automorphism Group ◽  
Semisimple Group ◽  
Picard Number ◽  
Projective Varieties ◽  
3 Dimensional

In the present work we describe 3-dimensional complexSL2-varieties where the genericSL2-orbit is a surface. We apply this result to classify the minimal 3-dimensional projective varieties with Picard-number 1 where a semisimple group acts such that the generic orbits are 2-dimensional.This is an ingredient of the classification [Keb99] of the 3-dimensional relatively minimal quasihomogeneous varieties where the automorphism group is not solvable.

A Classification of Homogeneous Surfaces

1981 ◽  
Vol 33 (5) ◽  
pp. 1097-1110 ◽  
Author(s):  
A. T. Huckleberry ◽  
E. L. Livorni
Keyword(s):  
Automorphism Group ◽  
Homogeneous Space ◽  
Lie Group ◽  
Compact Complex Manifold ◽  
Coset Space ◽  
Left Coset ◽  
Detailed Classification ◽  
Dimensional Ball ◽  
Lie Subgroup

Throughout this paper a surface is a 2-dimensional (not necessarily compact) complex manifold. A surface X is homogeneous if a complex Lie group G of holomorphic transformations acts holomorphically and transitively on it. Concisely, X is homogeneous if it can be identified with the left coset space G/H, where if is a closed complex Lie subgroup of G. We emphasize that the assumption that G is a complex Lie group is an essential part of the definition. For example, the 2-dimensional ball B2 is certainly “homogeneous” in the sense that its automorphism group acts transitively. But it is impossible to realize B2 as a homogeneous space in the above sense. The purpose of this paper is to give a detailed classification of the homogeneous surfaces. We give explicit descriptions of all possibilities.

Classification of AF Flows

2003 ◽  
Vol 46 (2) ◽  
pp. 164-177 ◽  
Author(s):  
Andrew J. Dean
Keyword(s):  
Dynamical Systems ◽  
Automorphism Group ◽  
Bratteli Diagram ◽  
Finite Dimensional

AbstractAn AF flow is a one-parameter automorphism group of an AF C*-algebra A such that there exists an increasing sequence of invariant finite dimensional sub-C*-algebras whose union is dense in A. In this paper, a classification of C*-dynamical systems of this form up to equivariant isomorphism is presented. Two pictures of the actions are given, one in terms of a modified Bratteli diagram/pathspace construction, and one in terms of a modified K0 functor.

scholarly journals Spherical subgroups in simple algebraic groups

2015 ◽  
Vol 151 (7) ◽  
pp. 1288-1308
Author(s):  
Friedrich Knop ◽  
Gerhard Röhrle
Keyword(s):  
Algebraic Group ◽  
Closed Subgroup ◽  
Positive Characteristic ◽  
Dense Orbit ◽  
Simple Algebraic Group ◽  
Spherical Subgroup ◽  
Group A ◽  
General Deformation ◽  
Characteristic 2

Let $G$ be a simple algebraic group. A closed subgroup $H$ of $G$ is said to be spherical if it has a dense orbit on the flag variety $G/B$ of $G$. Reductive spherical subgroups of simple Lie groups were classified by Krämer in 1979. In 1997, Brundan showed that each example from Krämer’s list also gives rise to a spherical subgroup in the corresponding simple algebraic group in any positive characteristic. Nevertheless, up to now there has been no classification of all such instances in positive characteristic. The goal of this paper is to complete this classification. It turns out that there is only one additional instance (up to isogeny) in characteristic 2 which has no counterpart in Krämer’s classification. As one of our key tools, we prove a general deformation result for subgroup schemes that allows us to deduce the sphericality of subgroups in positive characteristic from the same property for subgroups in characteristic zero.

scholarly journals The group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra

2019 ◽  
Vol 30 (11) ◽  
pp. 1950057 ◽  
Author(s):  
M. Izumi ◽  
T. Sogabe
Keyword(s):  
Automorphism Group ◽  
Vector Bundles ◽  
Group Structure ◽  
Cuntz Algebra ◽  
Classifying Space ◽  
Cuntz Algebras ◽  
K Theory ◽  
Continuous Fields

We determine the group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra [Formula: see text] for finite [Formula: see text] in terms of K-theory. We show that there is an example of a space for which the homotopy set is a noncommutative group, and hence, the classifying space of the automorphism group of the Cuntz algebra for finite [Formula: see text] is not an H-space. We also make an improvement of Dadarlat’s classification of continuous fields of the Cuntz algebras in terms of vector bundles.

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