Can I read Fundamentos da Geometria Complexa: aspectos geom\'etricos, topol\'ogicos e anal\'iticos on EtoBox?

Fundamentos da Geometria Complexa: aspectos geom\'etricos, topol\'ogicos e anal\'iticos by Sacchetto, Lucas Kaufmann is a scholarly article available to read on EtoBox.

What is Fundamentos da Geometria Complexa: aspectos geom\'etricos, topol\'ogicos e anal\'iticos about?

The main goal of this work is to present a detailed study of the foundations of Complex Geometry, highlighting its geometrical, 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 K\"ahler 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.

Author

Sacchetto, Lucas Kaufmann

Published

2012

Language

EN