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Invariant functions on Lie groups and Hamiltonian flows ofsurface group representations
Lie groups Hamiltonian flows
2015/9/29
In [7] it wasshown that ifn isthe fundamental group ofa closed oriented surface S
and Gis Lie group satisfying very general conditions, then the space Hom(n, G)/G
of conjugacy classes of representat...
Random Walks on Finite Groups
Finite Groups Random
2015/8/26
Markov chains on finite sets are used in a great variety of situations
to approximate, understand and sample from their limit distribution. A familiar
example is provided by card shuffling methods. ...
We prove many new cases of the Inverse Galois Problem for those simple groups arising fromorthogonal groups over finite fields. For example, we show that the finite simple groups Ω2n+1(p) and P&...
Universal covering spaces and fundamental groups in algebraic geometry as schemes
algebraic geometry fundamental groups
2015/7/14
In topology, the notions of the fundamental group
and the universal cover are closely intertwined. By importing
usual notions from topology into the algebraic and arithmetic setting, we construct a ...
The regularity conclusion in Lemma 1.4 is incorrect (G. Pappas gave a counterexample). Regularity of
X must be assumed as a hypothesis, and then the other conclusions follow (see below; also cf. [CEP...
Kashiwara de ned the notion of a crystal, and gave examples of crystal structures
associated with bases of representations of quantum groups. We recommend the
expository article Kashiwara [7], writt...
Automorphism groups of Calabi-Yau manifolds of Picard number two
Automorphism groups Calabi-Yau manifolds Picard number two Algebraic Geometry
2012/6/29
We prove that the automorphism group of an odd dimensional Calabi-Yau manifold of Picard number two is always a finite group. This makes a sharp contrast to the automorphism groups of K3 surfaces and ...
On reductive automorphism groups of regular embeddings
reductive automorphism groups regular embeddings Algebraic Geometry
2012/6/21
Let G be a connected reductive complex algebraic group acting on a smooth complete complex algebraic variety X. We assume that X under the action of G is a regular embedding, a condition satisfied in ...
Cyclic groups of automorphisms of complex K3 surfaces
Cyclic groups automorphisms complex K3 surfaces
2012/2/29
We determine all possible orders of automorphisms of complex K3 surfaces. A positive integer N is the order of an automorphism of a complex K3 surface if and only if \phi(N) \leq 20 and N is not 60, w...
Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups
Birational automorphism groups movable cone theorem Calabi-Yau manifolds of Wehler type
2011/9/22
Abstract: We prove that the birational automorphism group of any Calabi-Yau manifold given by a generic hypersurface of multi-degree two in $({\mathbf P^1})^{n+1}$ is isomorphic to the universal Coxet...
Beauville surfaces, moduli spaces and finite groups
Beauville surfaces moduli spaces finite groups Algebraic Geometry
2011/9/22
Abstract: In this paper we give the asymptotic growth of the number of connected components of the moduli space of surfaces of general type corresponding to certain families of Beauville surfaces with...
Representations of cyclic groups in positive characteristic and Weierstrass semigroups
Automorphisms Curves Differentials Numerical Semigroups
2011/9/20
Abstract: We study the $k[G]$-module structure of the space of holomorphic differentials of a curve defined over an algebraically closed field of positive characteristic, for a cyclic group $G$ of ord...
A Topological Version of the Borel-Tits Theorem on Abstract Homomorphisms of Simple Algebraic Groups
Topological Version Borel-Tits Theorem Simple Algebraic Groups
2010/12/9
In this paper, we produce topologized versions of two theorems. One is due to Borel and Tits [2] and is concerned with abstract homomorphisms of absolutely almost simple algebraic groups.