Vanishing Theorems and Effective Results in Algebraic Geometry

The School on Vanishing Theorems and Effective Results in Algebraic Geometry took place in ICTP, Trieste from 25 April 2000 to 12 May 2000. It was organized by J. P. Demailly (Université de Grenoble I) and R. Lazarsfeld (University of Michigan). The main topics considered were vanishing theorems, multiplyer ideal sheaves and effective results in algebraic geometry, tight closure, geometry of higher dimensional projective and Köhler manifolds, hyperbolic algebraic varieties. The school consisted of two weeks of lectures and one week of conference. This volume contains the lecture notes of most of the lectures in the first two weeks. Contents: Multiplier Ideal Sheaves and Analytic Methods in Algebraic Geometry by Jean-Pierre Demailly; Tight Closure and Vanishing Theorems by Karen E. Smith; The Base Point Free Theorem and the Fujita Conjecture by Stefan Helmke; Positivity of Direct Image Sheaves and Applications to Families of Higher Dimensional Manifolds by Eckart Viehweg; Subsheaves in the Tangent Bundle: Integrability, Stability and Positivity by Thomas Peternell; Geometry of Minimial Rational Curves on Fano Manifolds by Jun-Muk Hwang