Mathematische Annalen (MATH ANN )

Publisher: Springer Verlag


Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein David Hilbert Otto Blumenthal Erich Hecke Heinrich Behnke Hans Grauert und Heinz Bauer.

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    ABSTRACT: Let \(X\) be a Stein manifold of complex dimension at least two, \(F:X \rightarrow {{\mathbb {C}}}^n\) a local biholomorphism, and \(q\in F(X)\) . In this paper we formulate sufficient conditions, involving only objects naturally associated to \(q\) , in order for the fiber over \(q\) to be finite. Assume that \(F^{-1}(l)\) is \(1\) -connected for the generic complex line \(l\) containing \(q\) , and \(F^{-1}(l)\) has finitely many components whenever \(l\) is an exceptional line through \(q\) . Using arguments from topology and differential geometry, we establish a sharp estimate on the size of \(F^{-1}(q)\) . It follows that for \(n\ge 2\) a local biholomorphism of \(X\) onto \({{\mathbb {C}}}^n\) is invertible if and only if the pull-back of every complex line is \(1\) -connected.
    Mathematische Annalen 12/2014;
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    ABSTRACT: We study smooth hypersurfaces of degree \(d\ge n+1\) in \(\mathbf{P}^n\) whose spaces of smooth rational curves of low degrees are larger than expected, and show that under certain conditions, the primitive part of the middle cohomology of such hypersurfaces have non-trivial Hodge substructures. As an application, we prove that the space of lines on any smooth Fano hypersurface of degree \(d \le 8\) in \(\mathbf{P}^n\) has the expected dimension \(2n-d-3\) .
    Mathematische Annalen 12/2014; 360(3-4).
  • Mathematische Annalen 10/2014; 360(1-2).
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    ABSTRACT: Let k be a number field and F a function field in one variable over k. We prove that the ramification of a \(p\) -torsion element in \(Br\) ( \(F\) ) on a regular proper model over the ring of integers in \(k\) can be split in an extension of degree \(p^3\) . Using this result, we show that Colliot-Thélène’s conjecture on 0-cycles of degree 1 implies finiteness for the \(u\) -invariant of the function field of a curve over a totally imaginary number field and period-index bounds for the Brauer groups of arbitrary fields of transcendence degree 1 over the rational numbers.
    Mathematische Annalen 10/2014; 360(1-2).
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    ABSTRACT: The purpose of this paper is to establish Nadel type vanishing theorems with multiplier ideal sheaves of singular metrics admitting an analytic Zariski decomposition (such as, metrics with minimal singularities and Siu’s metrics). For this purpose, we generalize Kollár’s injectivity theorem to an injectivity theorem for line bundles equipped with singular metrics, by making use of the theory of harmonic integrals. Moreover we give asymptotic cohomology vanishing theorems for high tensor powers of line bundles.
    Mathematische Annalen 08/2014; 359(3).
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    ABSTRACT: In this paper, we study geometry of conformal minimal two-spheres immersed in quaternionic projective spaces. We firstly use Bahy-El-Dien and Wood’s results to obtain some characterizations of the harmonic sequences generated by conformal minimal immersions from \(S^2\) to the quaternionic projective space \({ HP}^2\) . Then we give a classification theorem of linearly full totally unramified conformal minimal immersions of constant curvature from \(S^2\) to the quaternionic projective space \({ HP}^2\) .
    Mathematische Annalen 08/2014; 359(3-4).
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    ABSTRACT: For every n≥3, we exhibit infinitely many extremal effective divisors on ℳ ¯ 1,n , the Deligne-Mumford moduli space parameterizing stable genus one curves with n ordered marked points.
    Mathematische Annalen 08/2014; 359(3).
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    ABSTRACT: Studying the (long-term) behavior of the K\"ahler-Ricci flow on mildly singular varieties, one is naturally lead to study weak solutions of degenerate parabolic complex Monge-Amp\'ere equations. The purpose of this article, the second of a series on this subject, is to develop a viscosity theory for degenerate complex Monge-Amp\'ere flows on compact K\"ahler manifolds. Our general theory allows in particular to define and study the (normalized) K\"ahler-Ricci flow on varieties with canonical singularities, generalizing results of Song and Tian.
    Mathematische Annalen 07/2014;
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    ABSTRACT: We derive an interpolation version of constrained matrix Li-Yau-Hamilton estimate on K\"ahler manifolds. As a result, we first get a constrained matrix Li-Yau-Hamilton estimate for heat equation on a K\"ahler manifold with fixed K\"ahler metric. Secondly, we get a corresponding estimate for forward conjugate heat equation on K\"ahler manifolds with time dependent K\"ahler metrics evolving by K\"ahler-Ricci flow.
    Mathematische Annalen 07/2014;
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    ABSTRACT: We prove the existence of small amplitude quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of the linear Airy equation. For Hamiltonian or reversible nonlinearities we also prove their linear stability. The key analysis concerns the reducibility of the linearized operator at an approximate solution, which provides a sharp asymptotic expansion of its eigenvalues. For quasi-linear perturbations this cannot be directly obtained by a KAM iteration. Hence we first perform a regularization procedure, which conjugates the linearized operator to an operator with constant coefficients plus a bounded remainder. These transformations are obtained by changes of variables induced by diffeomorphisms of the torus and pseudo-differential operators. At this point we implement a Nash-Moser iteration (with second order Melnikov non-resonance conditions) which completes the reduction to constant coefficients.
    Mathematische Annalen 06/2014; 359(1).
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    ABSTRACT: We characterize all Siegel cusp forms of degree n and large weight k by the growth of their Fourier coefficients. More precisely we prove, among other related results, that if the Fourier coefficients of a modular form on the congruence subgroup Γ 0 n (N) of square-free level N satisfy the “Hecke bound” at the cusp ∞, then it must be a cusp form, provided k>2n+1.
    Mathematische Annalen 06/2014; 359(1-2).
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    ABSTRACT: We solve the modified Kazdan-Warner problem of finding metrics with prescribed scalar curvature and unit total volume.
    Mathematische Annalen 04/2014;
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    ABSTRACT: For a proper open set [TEX equation: \Omega ] immersed in a metric space with the weak homogeneity property, and given a measure [TEX equation: \mu ] doubling on a certain family of balls lying “well inside” of [TEX equation: \Omega ] , we introduce a local maximal function and characterize the weights [TEX equation: w] for which it is bounded on [TEX equation: L^p(\Omega ,w d\mu )] when [TEX equation: 1 Document Type: Research Article DOI: Affiliations: 1: Instituto de Matemática Aplicada del Litoral, CONICET-UNL, Güemes 3450, 3000 , Santa Fe, Argentina, Email: 2: Instituto de Matemática Aplicada del Litoral, CONICET-UNL, Güemes 3450, 3000 , Santa Fe, Argentina, Email: 3: Instituto de Matemática Aplicada del Litoral, CONICET-UNL, Güemes 3450, 3000 , Santa Fe, Argentina, Email: Publication date: April 1, 2014 $(document).ready(function() { var shortdescription = $(".originaldescription").text().replace(/\\&/g, '&').replace(/\\, '<').replace(/\\>/g, '>').replace(/\\t/g, ' ').replace(/\\n/g, ''); if (shortdescription.length > 350){ shortdescription = "" + shortdescription.substring(0,250) + "... more"; } $(".descriptionitem").prepend(shortdescription); $(".shortdescription a").click(function() { $(".shortdescription").hide(); $(".originaldescription").slideDown(); return false; }); }); Related content In this: publication By this: publisher By this author: Harboure, Eleonor ; Salinas, Oscar ; Viviani, Beatriz GA_googleFillSlot("Horizontal_banner_bottom");
    Mathematische Annalen 04/2014; 358(3-4).
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    ABSTRACT: In this paper, we establish global $W^{2,p}$ estimates for solutions to the linearized Monge–Ampère equations under natural assumptions on the domain, Monge–Ampère measures and boundary data. Our estimates are affine invariant analogues of the global $W^{2,p}$ estimates of Winter for fully nonlinear, uniformly elliptic equations, and also linearized counterparts of Savin’s global $W^{2,p}$ estimates for the Monge–Ampère equations.
    Mathematische Annalen 04/2014; 358(3-4).