Introduction to Hodge Theory
نویسنده
چکیده
This course will present the basics of Hodge theory aiming to familiarize students with an important technique in complex and algebraic geometry. We start by reviewing complex manifolds, Kahler manifolds and the de Rham theorems. We then introduce Laplacians and establish the connection between harmonic forms and cohomology. The main theorems are then detailed: the Hodge decomposition and the Lefschetz decomposition. The Hodge index theorem, Hodge structures and polarizations are discussed. The non-compact case is also considered. Finally, time permitted, rudiments of the theory of variations of Hodge structures are given. Date: February 20, 2008.
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تاریخ انتشار 2008