Lectures on Vanishing Theorems

Introduction M. Kodaira''s vanishing theorem, saying that the inverse of an ample invert­ ible sheaf on a projective complex manifold X has no cohomology below the dimension of X and its generalization, due to Y. Akizuki and S. Nakano, have been proven originally by methods from differential geometry ([39J and [1]). Even if, due to J.P. Serre''s GAGA-theorems [56J and base change for field extensi...