On the zero-distribution of Epstein zeta-functions

We prove that the mean value of the real parts of the nontrivial zeros of the Epstein zeta-function associated with a positive definite quadratic form in n variables is equal to . Furthermore, we show that Epstein zeta-functions in general have an asymmetric zero-distribution with respect to the critical line Re .     

The space of complete embedded maximal surfaces with isolated singularities in the 3-dimensional Lorentz-Minkowski space

We prove that a complete embedded maximal surface in = (³, dx₁² + dx₂²-dx₃²) with a finite number of singularities is an entire maximal graph with conelike singularities over any spacelike plane, and so, it is asymptotic to a spacelike plane or a half catenoid. We show that the moduli space of entire maximal graphs over {x₃=0} in with n+12 singular points and vertical limit normal vector at infinity is a 3n+4-dimensional differentiable manifold. The convergence in means the one of conformal structures and Weierstrass data, and it is equivalent to the uniform convergence of graphs on compact subsets of {x₃=0}. Moreover, the position of the singular points in ³ and the logarithmic growth at infinity can be used as global analytical coordinates with the same underlying topology. We also introduce the moduli space of marked graphs with n+1 singular points (a mark in a graph is an ordering of its singularities), which is a (n+1)-sheeted covering of . We prove that identifying marked graphs differing by translations, rotations about a vertical axis, homotheties or symmetries about a horizontal plane, the corresponding quotient space is an analytic manifold of dimension 3n–1. This manifold can be identified with a spinorial bundle associated to the moduli space of Weierstrass data of graphs in .Mathematics Subject Classification (2000): 53C50, 58D10, 53C42First and second authors research partially supported by MEC-FEDER grant number MTM2004-00160Second and third authors research partially supported by Consejería de Educación y Ciencia de la Junta de Andalucía and the European Union.     

Order and algebra isomorphisms of spaces of regular operators

If E and F are real Banach lattices and there is an algebra and order isomorphism Φ:(E) →(F) between their respective ordered Banach algebras of regular operators then there is a linear order isomorphism U:E→F such that Φ(T) =UTU⁻¹ for all T ∈ (E).     

On the dynamics near infinity of some polynomial mappings in

We construct the Green current for a random iteration of horizontal-like mappings in . This is applied to the study of a polynomial map with the following properties: i. infinity is f-attracting; ii. f contracts the line at infinity to a point not in the indeterminacy set. We study for such mappings the escape rates near infinity, i.e. the set of possible values of the function We show in particular that the set of possible values can contain an interval. On the other hand the Green current T of f can be decomposed into pieces associated to an itinerary defined by the indeterminacy points. This allows us to prove that exists ||T||-a.e. and we give its value in terms of explicit quantities depending on f.     

Topological classification of holomorphic, semi-hyperbolic germs, in ``Quasi-Absence' of resonances

We give the classification, under topological conjugacy, of invertible holomorphic germs f:, with λ₁, . . . ,λ_n eigenvalues of d f₀, and |λ_i|≠1 for i=2, . . . ,n while λ₁ is a root of the unity, in the suitable hypothesis of ``quasi-absence' of resonances (i.e., assuming that for r_i≥0 and i=2, . . . ,n, with ).     

On topological Kadec norms

We present a topological analogue of the classic Kadec Renorming Theorem, as follows. Let be two separable metric topologies on the same set X. We prove that every point in X has an -neighbourhood basis consisting of sets that are -closed if and only if there exists a function φ: X→ℝ that is -lower semi-continuous and such that is the weakest topology on X that contains and that makes φ continuous. An immediate corollary is that the class of almost n-dimensional spaces consists precisely of the graphs of lower semi-continuous functions with at most n-dimensional domains.     

On the logarithmic plurigenera of complements of plane curves

Let B be a (not necessarily irreducible) plane curve in ². In the present article, we prove that if and only if Moreover, we determine the curve B when and Mathematics Subject Classification (2000): 14R05, 14H50, 14J26     

Integral varieties of the canonical cone structure on <Emphasis Type="Italic">G</Emphasis>/<Emphasis Type="Italic">P</Emphasis>

The canonical cone structure on a compact Hermitian symmetric space G/P is the fiber bundle where is the cone of the highest weight vectors under the action of the reductive part of P. It is known that the cone coincides with the cone of the vectors tangent to the lines in G/P passing through x, when we consider G/P as a projective variety under its homogeneous embedding into the projective space of the irreducible representation space V of G with highest weight associated to P. A subvariety X of G/P is said to be an integral variety of at all smooth points xG/P. Equivalently, an integral variety of is a subvariety of G/P whose embedded projective tangent space at each smooth point is a linear space We prove a kind of rigidity of the integral varieties under some dimension condition. After making a uniform setting to study the problem, we apply the theory of Lie algebra cohomology as a main tool. Finally we show that the dimension condition is necessary by constructing counterexamples.     

Characterisation of homogeneous polynomials which are constant on complex-tangential curves in the boundary of the unit ball of

We prove that a complex-tangential curve γ in the boundary of the unit ball of having the property that there exists a homogeneous polynomial P such that P=1 on γ has constant curvature. This implies that a homogeneous polynomial P having the property that there exists a closed complex-tangential curve γ (respectively a totally real 2-dimensional submanifold) in the boundary of the unit ball of such that P=1 on γ (respectively |P|=1 on γ) reduces to a monomial by a unitary chage of variables. These results represent a positive answer to conjectures of H. O. Kim.     

Analytic discs, plurisubharmonic hulls, and non-compactness of the -Neumann operator

We show that a complex manifold M in the boundary of a smooth bounded pseudoconvex domain Ω in is an obstruction to compactness of the -Neumann operator on Ω, provided that at some point of M, the Levi form of bΩ has the maximal possible rank n−1−dim(M) (i.e. the boundary is strictly pseudoconvex in the directions transverse to M). In particular, an analytic disc is an obstruction, provided that at some point of the disc, the Levi form has only one zero eigenvalue (i.e. the eigenvalue zero has multiplicity one). We also show that a boundary point where the Levi form has only one zero eigenvalue can be picked up by the plurisubharmonic hull of a set only via an analytic disc in the boundary. Research supported in part by NSF grant number DMS-0100517.     

Conjugacy classes of affine automorphisms of and linear automorphisms of ℙ n in the Cremona groups

We describe the conjugacy classes of affine automorphisms in the group Aut(n,) (respectively Bir()) of automorphisms (respectively of birational maps) of . From this we deduce also the classification of conjugacy classes of automorphisms of ℙⁿ in the Cremona group Bir().     

Dynamique des applications holomorphes propres de domaines réguliers et problème de l'injectivité

Summary This paper deals with proper holomorphic self-maps of smoothly bounded pseudoconvex domains in . We study the dynamical properties of their extension to the boundary and show that their non-wandering sets are always contained in the weakly pseudoconvex part of the boundary. In the case of complete circular domains, we combine this fact with an entropy/degree argument to show that the maps are automorphisms. Some of our results remain true in      

Log canonical thresholds of divisors on Grassmannians

Let L be the Plücker line bundle on the Grassmannian. Given D ∈ |kL|, we show that the log canonical threshold of D is at least . The main ingredients of the proof are Kapranov's result on the derived category of coherent sheaves on the Grassmannian, Nadel's vanishing theorem for multiplier ideal sheaves, and Demailly's vanishing theorem for vector bundles.     

An estimate on the supremum of a nice class of stochastic integrals and U-statistics

Let a sequence of iid. random variables ξ ₁, . . . ,ξ _n be given on a space with distribution μ together with a nice class of functions f(x ₁, . . . ,x _k ) of k variables on the product space For all f ∈ we consider the random integral J _n,k (f) of the function f with respect to the k-fold product of the normalized signed measure where μ _n denotes the empirical measure defined by the random variables ξ ₁, . . . ,ξ _n and investigate the probabilities for all x>0. We show that for nice classes of functions, for instance if is a Vapnik–Červonenkis class, an almost as good bound can be given for these probabilities as in the case when only the random integral of one function is considered. A similar result holds for degenerate U-statistics, too. Supported by the OTKA foundation Nr. 037886     

Un phénomène de concentration de genre

We show that the main part of the genus of the preimages of a projective line by a generic holomorphic endomorphism of goes to the support of the Green measure.

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Résumé Nous montrons que le genre des préimages dune droite projective par un endomorphisme holomorphe générique de se concentre sur le support de la mesure de Green.A phenomenon of concentration of genus

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Mathematics Subject Classification (2000): 32H50, 32U40, 32Q45     

Restriction of the cotangent bundle to elliptic curves and Hilbert-Kunz functions

We describe the possible restrictions of the cotangent bundle to an elliptic curve . We apply this in positive characteristic to the computation of the Hilbert-Kunz function of a homogeneous R₊-primary ideal in the graded section ring .     

A branch-and-cut algorithm for the stochastic uncapacitated lot-sizing problem

This paper addresses a multi-stage stochastic integer programming formulation of the uncapacitated lot-sizing problem under uncertainty. We show that the classical (ℓ,S) inequalities for the deterministic lot-sizing polytope are also valid for the stochastic lot-sizing polytope. We then extend the (ℓ,S) inequalities to a general class of valid inequalities, called the inequalities, and we establish necessary and sufficient conditions which guarantee that the inequalities are facet-defining. A separation heuristic for inequalities is developed and incorporated into a branch-and-cut algorithm. A computational study verifies the usefulness of the inequalities as cuts. This research has been supported in part by the National Science Foundation under Award number DMII-0121495.     

Commutativity of Almost <Emphasis Type="Italic">F</Emphasis>-algebras

Let A be an Archimedean vector lattice, let be its Dedekind completion and let B be a Dedekind complete vector lattice. If Ψ ₀:A × A→ B is a positive orthosymmetric bimorphism, then there exists a positive bimorphism extension Ψ of Ψ ₀ to × in B which is orthosymmetric. This leads to a new and short proof of the commutativity of the almost f-algebras multiplications.     

A class of <Emphasis Type="Italic">p</Emphasis>-adic Galois representations arising from abelian varieties over

Let V be a p-adic representation of the absolute Galois group G of that becomes crystalline over a finite tame extension, and assume p2. We provide necessary and sufficient conditions for V to be isomorphic to the p-adic Tate module V_p() of an abelian variety defined over . These conditions are stated on the filtered (,G)-module attached to V.Mathematics Subject Classification (2000): 14F30, 11G10, 11F80, 14G20, 14F20     

The theory of energy for sub-Laplacians with an application to quasi-continuity

In this paper, we provide a suitable theory for the energy where μ is a Radon measure and Γ is the fundamental solution of a sub-Laplacian on a stratified group As a significant application, we prove the quasi-continuity of superharmonic functions related to . The proofs are elementary and mostly rely on the use of appropriate mean-value formulas and mean-integral operators relevant to the Potential Theory for .