This course will develop the parallel between the geometry of a compact, oriented differentiable manifold M endowed with a Riemannian metric and the geometry of a compact (oriented) complex manifold M with a Riemannian metric compatible with the complex structure. Such a metric is called a Kähler metric for M.
This is a modern introduction to Kaehlerian geometry and Hodge structure.
The exposition is as accessible as possible and doesn't require a deep background. At the same time, the book presents some topics at the forefront of current research. The book is divided between introductory and advanced lectures.
This is a version of the Jacobson— Morosov theorem. EXERCISE A.3.7 Let N C g[(V) be nilpotent and Y C g[(V) be semisimple. Set V4 I E4 Then the following are equivalent: (1) There exists an slg—triple {N+, NI, Y} with N+ I N. (2) The ...
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Offers an examination of the precursors of Hodge theory: first, the studies of elliptic and abelian integrals by Cauchy, Abel, Jacobi, and Riemann; and then the studies of two-dimensional multiple integrals by Poincare and Picard.
The text is complemented by exercises which provide useful results in complex algebraic geometry.
Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.
The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art.
Hodge theory is a standard tool in characterizing differ- ential complexes and the topology of manifolds. This book is a study of the Hodge-Kodaira and related decompositions on manifolds with boundary under mainly analytic aspects.
Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)