Lectures on vanishing theorems

About “Lectures on vanishing theorems”

This book is a collection of lectures given at the DMV-Seminar "Algebraic Geometry, 1991" at Schloss Reisensburg. It focuses on Kodaira's vanishing theorem and related generalizations, using an algebraic approach. The text covers logarithmic de Rham complexes, spectral sequences, lifting properties for manifolds, and the proof of the degeneration of the Hodge to de Rham spectral sequence. It also includes applications of vanishing theorems and methods from characteristic p geometry. The exposition is self-contained and assumes a background in modern algebraic geometry. An appendix provides necessary background on cohomology theory. The contents include topics such as invertible sheaves, differential forms, characteristic p methods, and generic vanishing theorems.