On the Orders of the Automorphism Groups of Certain Projective Manifolds

1981 ◽  
pp. 145-158 ◽  
Author(s):  
Alan Howard ◽  
Andrew John Sommese
Keyword(s):  
Automorphism Groups ◽  
Projective Manifolds

scholarly journals Algebraically hyperbolic manifolds have finite automorphism groups

2019 ◽  
Vol 22 (02) ◽  
pp. 1950003
Author(s):  
Fedor A. Bogomolov ◽  
Ljudmila Kamenova ◽  
Misha Verbitsky
Keyword(s):  
Positive Constant ◽  
Classical Result ◽  
Automorphism Groups ◽  
Hyperbolic Manifolds ◽  
Projective Manifold ◽  
Kobayashi Hyperbolicity ◽  
Genus Formula ◽  
Projective Manifolds

A projective manifold [Formula: see text] is algebraically hyperbolic if there exists a positive constant [Formula: see text] such that the degree of any curve of genus [Formula: see text] on [Formula: see text] is bounded from above by [Formula: see text]. A classical result is that Kobayashi hyperbolicity implies algebraic hyperbolicity. It is known that Kobayashi hyperbolic manifolds have finite automorphism groups. Here, we prove that, more generally, algebraically hyperbolic projective manifolds have finite automorphism groups.

scholarly journals ORBIFOLD ASPECTS OF CERTAIN OCCULT PERIOD MAPS

2019 ◽  
pp. 1-20 ◽  
Author(s):  
ZHIWEI ZHENG
Keyword(s):  
Automorphism Groups ◽  
Small Dimension ◽  
Hodge Structures ◽  
Cubic Surfaces ◽  
Cyclic Covers ◽  
Projective Manifolds ◽  
Complex Projective

We first characterize the automorphism groups of Hodge structures of cubic threefolds and cubic fourfolds. Then we determine for some complex projective manifolds of small dimension (cubic surfaces, cubic threefolds, and nonhyperelliptic curves of genus $3$ or $4$ ), the action of their automorphism groups on Hodge structures of associated cyclic covers, and thus confirm conjectures made by Kudla and Rapoport in (Pacific J. Math. 260(2) (2012), 565–581).

scholarly journals Discrete automorphism groups of convex cones of finite type

2014 ◽  
Vol 150 (11) ◽  
pp. 1939-1962 ◽  
Author(s):  
Eduard Looijenga
Keyword(s):  
Algebraic Geometry ◽  
Finite Type ◽  
Convex Cone ◽  
Fundamental Domain ◽  
Automorphism Groups ◽  
Convex Cones ◽  
Weyl Groups ◽  
Arithmetic Groups ◽  
Dual Cones ◽  
Projective Manifolds

AbstractWe investigate subgroups of $\text{SL}(n,\mathbb{Z})$ which preserve an open nondegenerate convex cone in $\mathbb{R}^{n}$ and admit in that cone as fundamental domain a polyhedral cone of which some faces are allowed to lie on the boundary. Examples are arithmetic groups acting on self-dual cones, Weyl groups of certain Kac–Moody algebras, and they do occur in algebraic geometry as the automorphism groups of projective manifolds acting on their ample cones.

Pentavalent 1-Transitive Digraphs with Non-Solvable Automorphism Groups

2020 ◽  
Vol 51 (4) ◽  
pp. 1919-1930
Author(s):  
Masoumeh Akbarizadeh ◽  
Mehdi Alaeiyan ◽  
Raffaele Scapellato
Keyword(s):  
Automorphism Groups

scholarly journals Serre’s Property (FA) for automorphism groups of free products

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Naomi Andrew
Keyword(s):  
Automorphism Group ◽  
Free Product ◽  
Finite Groups ◽  
Automorphism Groups ◽  
Sufficient Conditions ◽  
Free Products ◽  
Cyclic Groups ◽  
Link Type ◽  
Open Case

AbstractWe provide some necessary and some sufficient conditions for the automorphism group of a free product of (freely indecomposable, not infinite cyclic) groups to have Property (FA). The additional sufficient conditions are all met by finite groups, and so this case is fully characterised. Therefore, this paper generalises the work of N. Leder [Serre’s Property FA for automorphism groups of free products, preprint (2018), https://arxiv.org/abs/1810.06287v1]. for finite cyclic groups, as well as resolving the open case of that paper.

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