Fundamentos da geometria complexa: aspectos geométricos, topológicos e analiticos. / Foundations of Complex Geometry: geometric, topological and analytic aspects.

AUTOR(ES)
FONTE

IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia

DATA DE PUBLICAÇÃO

03/05/2012

RESUMO

The main goal of this work is to present a detailed study of the foundations of Complex Geometry, highlighting its geometric, topological and analytical aspects. Beginning with a preliminary material, such as the basic results on holomorphic functions in one or more variables and the definition and first examples of a complex manifold, we move on to an introduction to sheaf theory and its cohomology, an essential tool to the rest of the work. After a discussion on divisors and line bundles we turn attention to Kähler Geometry and its central results, such as the Hodge Decomposition Theorem, the Hard Lefschetz Theorem and the Lefschetz Theorem on $(1,1)$-classes. After that, we study complex vector bundles and its geometry, focusing on the concepts of connections, curvature and Chern classes. Finally, we finish by describing some aspects of the topology of complex manifolds, such as the Lefschetz Hyperplane Theorem and some of its consequences.

ASSUNTO(S)

teorema da decomposição de hodge lefschetz theorem on (1 1)-classes leschetz hyperplane theorem. sheaf cohomology teorema das (1 1) -classes de lefschetz teorema dos hiperplanos de lefschetz teorema ``difícil de lefschetz variedades de kähler chern classes classes de chern cohomologia de feixes complex geometry geometria complexa hard lefschetz theorem hodge decomposition theorem kähler manifolds

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