Title: Linear systems and vanishing theorems

Time: June 5-July 2 1998

Professor: Lawrence Ein (University of Illinois at Chicago)

Collaborator: Vlaidimir Masek (Washington University)

Place: Department of Mathematics University of Catania

Scientific program: Linear systems have played a very important role in algebraic geometry. In the 50's and 60's, Serre, Kodaira, Grothendieck Griffiths and others developed the theory of ample line bundles. In the recent years, linear systems played a central role in the theory of higher dimension geometry as developed by Mori, Kawamata , Shokurov, Miyaoka, Kollar and others. Two of the basic tools in this study are the vanishing theorem and the base-points free theorem. In this course, we will give a survey of these results. We'll discuss the basic tools. We'll learn about some of the recent progresses and open questions about effective results concerning linear systems.