- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 12:23:03
9
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=CMH&vol=80&iss=2&update_since=2024-03-28
Commentarii Mathematici Helvetici
Comment. Math. Helv.
CMH
0010-2571
1420-8946
General
10.4171/CMH
http://www.ems-ph.org/doi/10.4171/CMH
subscribers, moving wall 5 years
European Mathematical Society Publishing House
Zuerich, Switzerland
© Swiss Mathematical Society
80
2005
2
Line bundles on complex tori and a conjecture of Kodaira
Jean-Pierre
Demailly
Université Grenoble I, SAINT MARTIN D'HERES CEDEX, FRANCE
Thomas
Eckl
Universität Köln, KÖLN, GERMANY
Thomas
Peternell
Universität Bayreuth, BAYREUTH, GERMANY
Kähler manifold, deformation, vector bundles
Several complex variables and analytic spaces
General
229
242
10.4171/CMH/13
http://www.ems-ph.org/doi/10.4171/CMH/13
Hilbert modular foliations on the projective plane
L.
Mendes
, RIO DE JANEIRO, BRAZIL
Jorge Vitório
Pereira
Estrada Dona Castorina 110, RIO DE JANEIRO RJ, BRAZIL
Holomorphic foliation, Kodaira dimension, Hilbert modular surfaces
We describe explicitly holomorphic singular foliations on the projective plane corresponding to natural foliations of Hilbert modular surfaces associated to the field Q. These are concrete models for a very special class of foliations in the recent birational classification of foliations on projective surfaces.
Partial differential equations
Algebraic geometry
General
243
291
10.4171/CMH/14
http://www.ems-ph.org/doi/10.4171/CMH/14
The macroscopic spectrum of nilmanifolds with an emphasis on the Heisenberg groups
Constantin
Vernicos
Université Montpellier 2, MONTPELLIER CEDEX, FRANCE
Spectrum of the Laplacian, nilmanifolds, homogenization, stable norm, asymptotic volume, Albanese metric, rigidity
Take a Riemannian nilmanifold, lift its metric on its universal cover. In that way one obtains a metric invariant under the action of some co-compact subgroup. We use it to define metric balls and then study the spectrum of the Dirichlet Laplacian. Using homogenization techniques we describe the asymptotic behavior of the spectrum when the radius of these balls goes to infinity. This involves the spectrum, which we call macroscopic spectrum, of a so called homogenized operator on a specific domain. Furthermore we show that the first macroscopic eigenvalue is bounded from above, by a universal constant in the case of the three dimensional Heisenberg group, and by a constant depending on the Albanese torus for the other nilmanifolds. We also show that the Heisenberg groups belong to a family of nilmanifolds, where the equality characterizes some pseudo-left-invariant metrics.
Differential geometry
Global analysis, analysis on manifolds
Mechanics of deformable solids
General
293
315
10.4171/CMH/15
http://www.ems-ph.org/doi/10.4171/CMH/15
Topological symmetry groups of graphs embedded in the 3-sphere
Erica
Flapan
Pomona College, CLAREMONT, UNITED STATES
Ramin
Naimi
Occidental College, LOS ANGELES, UNITED STATES
James
Pommersheim
Reed College, PORTLAND, UNITED STATES
Harry
Tamvakis
Brandeis University, WALTHAM, UNITED STATES
Topological symmetry group, automorphism group, embedded graph, spatial graph, 3-connected graph
The topological symmetry group of a graph embedded in the $3$-sphere is the group consisting of those automorphisms of the graph which are induced by some homeomorphism of the ambient space. We prove strong restrictions on the groups that can occur as the topological symmetry group of some embedded graph. In addition, we characterize the orientation preserving topological symmetry groups of embedded $3$-connected graphs in the $3$-sphere.
Combinatorics
Global analysis, analysis on manifolds
Mechanics of deformable solids
General
317
354
10.4171/CMH/16
http://www.ems-ph.org/doi/10.4171/CMH/16
Quelques nouveaux phénomènes de rang 1 pour les groupes de difféomorphismes du cercle
Andrés
Navas
Universidad de Santiago de Chile, SANTIAGO, CHILE
Rigidity, group cohomology, circle diffeomorphisms
Nous démontrons un théorème de super-rigidité pour les actions de réseaux de rang supérieur par difféomorphismes du cercle. We prove a superrigidity theorem for actions of higher rank lattices by diffeomorphisms of the circle.
Manifolds and cell complexes
Global analysis, analysis on manifolds
Topological groups, Lie groups
Dynamical systems and ergodic theory
355
375
10.4171/CMH/17
http://www.ems-ph.org/doi/10.4171/CMH/17
Vanishing and non-vanishing for the first $L^p$-cohomology of groups
Marc
Bourdon
Université Lille I, VILLENEUVE D'ASCQ CEDEX, FRANCE
Florian
Martin
Philip Morris International, NEUCHÂTEL, SWITZERLAND
Alain
Valette
Université de Neuchâtel, NEUCHÂTEL, SWITZERLAND
Group cohomology, $L^p$-cohomology, $CAT(-1)$ space, critical exponent
We prove two results on the first $L^p$-cohomology $\overline{H}^{1}_{(p)}(\Gamma)$ of a finitely generated group $\Gamma$: \begin{enumerate} \item [1)] If $N\subset H\subset\Gamma$ is a chain of subgroups, with $N$ non-amenable and normal in $\Gamma$, then $\overline{H}^{1}_{(p)}(\Gamma)=0$ as soon as $\overline{H}^{1}_{(p)}(H)=0$. This allows for a short proof of a result of L\"uck \cite{LucMatAnn}: if $N\lhd\Gamma$, $N$ is infinite, finitely generated as a group, and $\Gamma/N$ contains an element of infinite order, then $\overline{H}^{1}_{(2)}(\Gamma)=0$. \item [2)] If $\Gamma$ acts isometrically, properly discontinuously on a proper $CAT(-1)$ space $X$, with at least 3 limit points in $\partial X$, then for $p$ larger than the critical exponent $e(\Gamma)$ of $\Gamma$ in $X$, one has $\overline{H}^{1}_{(p)}(\Gamma)\neq 0$. As a consequence we extend a result of Shalom \cite{Sha}: let $G$ be a cocompact lattice in a rank 1 simple Lie group; if $G$ is isomorphic to $\Gamma$, then $e(G)\leq e(\Gamma)$. \end{enumerate}
Group theory and generalizations
Abstract harmonic analysis
Manifolds and cell complexes
General
377
389
10.4171/CMH/18
http://www.ems-ph.org/doi/10.4171/CMH/18
Optimal $SL(2)$-homomorphisms
George
McNinch
Tufts University, MEDFORD, UNITED STATES
Reductive group, nilpotent orbit, instability flag, completely reducible subgroup, principal homomorphism
Let $G$ be a semisimple group over an algebraically closed field of \emph{very good} characteristic for $G$. In the context of geometric invariant theory, G. Kempf and -- independently -- G. Rousseau have associated optimal cocharacters of $G$ to an unstable vector in a linear $G$-representation. If the nilpotent element $X \in \Lie(G)$ lies in the image of the differential of a homomorphism $\SL_2 \to G$, we say that homomorphism is optimal for $X$, or simply optimal, provided that its restriction to a suitable torus of $\SL_2$ is optimal for $X$ in the sense of geometric invariant theory. We show here that any two $\SL_2$-homomorphisms which are optimal for $X$ are conjugate under the connected centralizer of $X$. This implies, for example, that there is a unique conjugacy class of \emph{principal homomorphisms} for $G$. We show that the image of an optimal $\SL_2$-homomorphism is a \emph{completely reducible} subgroup of $G$; this is a notion defined recently by J-P. Serre. Finally, if $G$ is defined over the (arbitrary) subfield $K$ of $k$, and if $X \in \Lie(G)(K)$ is a $K$-rational nilpotent element with $X^{[p]}=0$, we show that there is an optimal homomorphism for $X$ which is defined over $K$.
Group theory and generalizations
General
391
426
10.4171/CMH/19
http://www.ems-ph.org/doi/10.4171/CMH/19
Transcendental submanifolds of ${\mathbb R}{\mathbb P}^n$
Selman
Akbulut
Michigan State University, EAST LANSING, UNITED STATES
Henry
King
University of Maryland, COLLEGE PARK, UNITED STATES
Real algebraic sets
In this paper we give examples of closed smooth submanifolds of $\R\P^{n}$ which are isotopic to nonsingular projective subvarieties of $\R\P^{n}$ but they can not be isotopic to the real parts of nonsingular complex projective subvarieties of $\C\P^{n}$.
Manifolds and cell complexes
General
427
432
10.4171/CMH/20
http://www.ems-ph.org/doi/10.4171/CMH/20
Une caractérisation des endomorphismes de Lattès par leur mesure de Green
F.
Berteloot
Université Paul Sabatier, TOULOUSE CEDEX, FRANCE
C.
Dupont
Université Paris Sud, ORSAY CEDEX, FRANCE
Lattès endomorphisms, linearization, maximal entropy mesaure, Hausdorff dimension, Liapounov exponents
We show that the Lattès endomorphisms are the only holomorphic endomorphisms of the complex $k$-dimensional projective space whose measure of maximal entropy is absolutely continuous with respect to the Lebesgue measure. As a consequence, Lattès endomorphisms are also characterized by other extremal properties as the maximality of the Hausdorff dimension of their measure of maximal entropy or the minimality of their Liapounov exponents. Our proof uses a linearization method which is of independant interest and a previous characterization by the regularity of the Green current.
Several complex variables and analytic spaces
General
433
454
10.4171/CMH/21
http://www.ems-ph.org/doi/10.4171/CMH/21