Lectures on Vanishing Theorems

Description

This work - an extended collection of lectures delivered at "Schloss Reisenburg" during the DMV-Seminar, "Algebraic Geometry, 1991" - aims to present Kodaira's vanishing theorem and several generalizations in a way which is as algebraic as possible. Together, the lectures develop the theory of logarithmic de Rham complexes, the use of the corresponding spectral sequence, lifting properties for manifolds and their Frobenius morphisms in characteristic p>0 and the proof of the degeneration of the Hodge to de Rham spectral sequence with algebraic methods, due to P. Deligne and L. Illusie. These methods are applied to obtain vanishing theorems.

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