22nd Autumn School in Algebraic Geometry

Wykno (Poland), September 6 - 11, 1999

Teachers: Marco Andreatta (Universita di Trento), Massimiliano Mella (Universita di Ferrara).

Title: Morphisms of Projective Varieties from the viewpoint of Minimal Model Theory

1. Vanishing and non-vanishing theorems: resolving the base locus of linear systems - from the classical arguments toward the new techniques of Kawamata and others, existence of good sections of the (pluri-)anticanonical system and the Apollonius method.
2. Fano-Mori contractions: definitions, classical facts and questions, rational curves on algebraic varieties, existence of rational curves in fibers of a Fano-Mori contraction, classification of Fano-Mori contractions.
3. Applications: minimal model program, adjunction theory, Moishezon manifolds, projective varieties with an action of a linear algebraic group, birational geometry of uniruled varieties.

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