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Summary: MORPHISMS OF PROJECTIVE VARIETIES FROM THE
VIEWPOINT OF MINIMAL MODEL THEORY
MARCO ANDREATTA AND MASSIMILIANO MELLA
Contents
Introduction 2
Part 1. Preliminaries 3
1.1. The Kleiman{Mori cone of a projective variety. 3
1.2. Fujita genus 7
Part 2. Base point free technique 9
2.1. Base point freeness 9
2.2. Singularities and log singularities. 14
2.2.1. How to use singularities and the CLC locus to prove base
point free-type theorems 16
2.3. Exercises-Examples 17
Part 3. Fano-Mori or extremal contractions 18
3.1. Contractions associated to a ray of the Kleiman{Mori cone 18
3.1.1. Local Contraction 20
3.2. Examples. 20
3.3. Relative Base point freeness on Fano-Mori Contractions 23
Part 4. Biregular geometry 28
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