### 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

**Program:**

**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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