E-Book, Englisch, 312 Seiten
Ancona / Gaveau Differential Forms on Singular Varieties
1. Auflage 2005
ISBN: 978-1-4200-2652-8
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
De Rham and Hodge Theory Simplified
E-Book, Englisch, 312 Seiten
Reihe: Chapman & Hall/CRC Pure and Applied Mathematics
ISBN: 978-1-4200-2652-8
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
Differential Forms on Singular Varieties: De Rham and Hodge Theory Simplified uses complexes of differential forms to give a complete treatment of the Deligne theory of mixed Hodge structures on the cohomology of singular spaces. This book features an approach that employs recursive arguments on dimension and does not introduce spaces of higher dimension than the initial space. It simplifies the theory through easily identifiable and well-defined weight filtrations. It also avoids discussion of cohomological descent theory to maintain accessibility. Topics include classical Hodge theory, differential forms on complex spaces, and mixed Hodge structures on noncompact spaces.
Zielgruppe
Theoretical and applied mathematicians and advanced students.
Autoren/Hrsg.
Weitere Infos & Material
Classical Hodge Theory. Spectral Sequences and Mixed Hodge Structures. Complex Manifolds, Vector Bundles, Differential Forms. Sheaves and Cohomology. Harmonic Forms on Hermitian Manifolds. Hodge Theory on Compact Kählerian Manifolds. The Theory of Residues on a Smooth Divisor. Complex Spaces. Differential Forms on Complex Spaces. The Basic Example. Differential Forms in Complex Spaces. Mixed Hodge Structures on Compact Spaces. Mixed Hodge Structures on Noncompact Spaces. Residues and Hodge Mixed Structures: Leray Theory. Residues and Mixed Hodge Structures on Noncompact Manifolds. Mixed Hodge Structures in Noncompact Spaces: The Basic Example. Mixed Hodge Structures on Noncompact Singular Spaces.
