Search results for "Automorphism"

Automorphism Groups of Certain Rational Hypersurfaces in Complex Four-Space

2014

The Russell cubic is a smooth contractible affine complex threefold which is not isomorphic to affine three-space. In previous articles, we discussed the structure of the automorphism group of this variety. Here we review some consequences of this structure and generalize some results to other hypersurfaces which arise as deformations of Koras–Russell threefolds.

Quotients of the Dwork Pencil

2012

In this paper we investigate the geometry of the Dwork pencil in any dimension. More specifically, we study the automorphism group G of the generic fiber of the pencil over the complex projective line, and the quotients of it by various subgroups of G. In particular, we compute the Hodge numbers of these quotients via orbifold cohomology.

Groups acting freely on Calabi-Yau threefolds embedded in a product of del Pezzo surfaces

2011

In this paper, we investigate quotients of Calabi-Yau manifolds $Y$ embedded in Fano varieties $X$, which are products of two del Pezzo surfaces — with respect to groups $G$ that act freely on $Y$. In particular, we revisit some known examples and we obtain some new Calabi-Yau varieties with small Hodge numbers. The groups $G$ are subgroups of the automorphism groups of $X$, which is described in terms of the automorphism group of the two del Pezzo surfaces.

Automorphisms of Hyperelliptic GAG-codes

2008

In this talk, we discuss the n-automorphism groups of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic function fields. Such groups are, up to isomorphism, subgroups of the automorphism groups of the underlying function fields. We also present some examples in which the n-automorphism groups can be determined explicitly.

From resurgent functions to real resummation through combinatorial Hopf algebras

2014

Pas de résumé en anglais.

On the automorphism group of the integral group ring of Sk wr Sn

1992

Abstract Let G = SkwrSn be the wreath product of two symmetric groups Sk and Sn. We prove that every normalized automorphism θ of the integral group ring Z G can be written in the form θ = γ ° τu, where γ is an automorphism of G and τu denotes the inner automorphism induced by a unit u in Q G.

Automorphisms of the integral group ring of the hyperoctahedral group

1990

The purpose of this paper is to verify a conjecture of Zassenhaus [3] for hyperoctahedral groups by proving that every normalized automorphism () of ZG can be written in the form () = Tu 0 I where I is an automorphism of ZG obtained by extending an automorphism of G linearly to ZG and u is a unit of (JJG. A similar result was proved for symmetric groups by Peterson in [2]; the reader should consult [3] or the survey [4] for other results of this kind. 1989

Automorphisms of the integral group rings of some wreath products

1991

Transitive factorizations in the hyperoctahedral group

2008

The classical Hurwitz enumeration problem has a presentation in terms of transitive factor- izationsin the symmetric group. This presentationsuggestsageneralizationfromtypeAto otherfinite reflection groups and, in particular, to type B.W e study this generalization both from ac ombinatorial and a geometric point of view, with the prospect of providing am eans of understanding more of the structure of the moduli spaces of maps with an S2-symmetry. The type A case has been well studied and connects Hurwitz numbers to the moduli space of curves. W ec onjecture an analogous setting for the type B case that is studied here. 1I ntroduction Transitive factorizations of permutations into transposit…

The McKay conjecture and Galois automorphisms

2004

The main problem of representation theory of finite groups is to find proofs of several conjectures stating that certain global invariants of a finite group G can be computed locally. The simplest of these conjectures is the ?McKay conjecture? which asserts that the number of irreducible complex characters of G of degree not divisible by p is the same if computed in a p-Sylow normalizer of G. In this paper, we propose a much stronger version of this conjecture which deals with Galois automorphisms. In fact, the same idea can be applied to the celebrated Alperin and Dade conjectures.