On the cohomology of pseudoeffective line bundles

The goal of this survey is to present various results concerning the cohomology of pseudoeffective line bundles on compact K{\"a}hler manifolds, and related properties of their multiplier ideal sheaves. In case the curvature is strictly positive, the prototype is the well known Nadel vanishing theorem, which is itself a generalized analytic version of the fundamental Kawamata-Viehweg vanishing theorem of algebraic geometry. We are interested here in the case where the curvature is merely semipositive in the sense of currents, and the base manifold is not necessarily projective. In this situation, one can still obtain interesting information on cohomology, e.g. a Hard Lefschetz theorem with pseudoeffective coefficients, in the form of a surjectivity statement for the Lefschetz map. More recently, Junyan Cao, in his PhD thesis defended in Grenoble, obtained a general K{\"a}hler vanishing theorem that depends on the concept of numerical dimension of a given pseudoeffective line bundle. The proof of these results depends in a crucial way on a general approximation result for closed (1,1)-currents, based on the use of Bergman kernels, and the related intersection theory of currents. Another important ingredient is the recent proof by Guan and Zhou of the strong openness conjecture. As an application, we discuss a structure theorem for compact K{\"a}hler threefolds without nontrivial subvarieties, following a joint work with F.Campana and M.Verbitsky. We hope that these notes will serve as a useful guide to the more detailed and more technical papers in the literature; in some cases, we provide here substantially simplified proofs and unifying viewpoints.Comment: 39 pages. This survey is a written account of a lecture given at the Abel Symposium, Trondheim, July 201

Stereoselective synthesis of 2,5-disubstituted-1,4-oxathiane S-oxides

beta-Allyloxy and beta-propargyloxy tert-butyl sulfoxides undergo tandem sulfoxide eliminination-intramolecular sulfenic acid addition reactions to produce 1,4-oxathiane S-oxides

Domains of definition of Monge-Ampère operators on compact Kähler manifolds

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Adição de alanina, glicina e glutamina ao meio crioprotetor seminal de garanhões Mangalarga Marchador Addition of alanine, glycine and glutamine to frozen seminal extender from Mangalarga Marchador stallions

Objetivou-se neste trabalho verificar o efeito da adição de alanina, glicina e glutamina ao meio crioprotetor seminal de garanhões Mangalarga Marchador. Foram utilizados cinco garanhões provenientes do haras Lugavi. Três ejaculados de cada garanhão, após coleta e avaliação, foram divididos em seis tratamentos: sem adição de aminoácidos, adição de 40 mM de alanina, adição de 40 mM de glicina, adição de 60 mM de glutamina, adição de 7 mM de alanina + 7 mM de glicina + 20 mM de glutamina e adição de 40 mM de alanina + 40 mM de glicina + 60 mM de glutamina ao diluente de congelamento convencional. Foram avaliados os parâmetros motilidade total, motilidade progressiva, retidão, linearidade, velocidade média do percurso, velocidade linear, velocidade curvilínea, amplitude lateral de cabeça e frequência de batimentos dos espermatozoides por meio de análise espermática assistida por computador (CASA), funcionalidade da membrana plasmática por choque hiposmótico e integridade de membrana acrossomal pelo teste FITC-PSA. Não houve melhora nos parâmetros de motilidade e cinética espermática nem na funcionalidade de membrana, entretanto, a adição de aminoácidos ao meio crioprotetor seminal aumentou o número de espermatozoides com membrana acrossomal íntegra. Os melhores resultados neste teste são obtidos com 40 mM de alanina (78,6 ± 13,6), 40 mM de glicina (74,7 ± 19,6) ou 7 mM de alanina + 7 mM de glicina + 20 mM de glutamina (76,8 ± 17,5), porém outros estudos devem ser realizados para determinação da concentração ideal desses componentes.<br>The objective of this study was to analyze the effect of the addition of alanine, glycine and glutamine on frozen seminal extender of Mangalarga marchador breed stallions. Five stallions were used from the Lugavi stables. Three ejaculates from each stallion were divided into six treatments: without the addition of amino acids, addition of 40 mM alanine, addition of 40 mM glycine, addition of 60 mM glutamine, addition of 7 mM glycine, alanine 7 mM + 20 mM glutamine and addition of 40 mM of glycine + 40 mM of alanine + 60 mM of glutamine to conventional frozen extender. The parameters evaluated were total motility, progressive motility, straightness, linearity, path velocity, progressive velocity, track speed, lateral amplitude and beat frequency by computer assisted sperm analysis (CASA), functionality of plasmatic membrane by hypo-osmotic shock and acrossomal membrane integrity by the FITC-PSA test. No improvement was found in the kinematic parameters and sperm motility and nor in membrane functionality but the addition of amino acids to seminal extender resulted in a higher integrity of the acrossomal membrane. The best results obtained in this test are with 40 mM alanine (78.6 ± 13.6), 40 mM glycine (74.7 ± 19.6) or 7 mM glycine, alanine 7 mM + 20 mM glutamine (76.8 ± 17.5), however, more studies should be conducted to reach the ideal concentration of these components