Summary: AN INTRODUCTION TO MORI THEORY:
THE CASE OF SURFACES
MARCO ANDREATTA
Contents
Introduction 1
Part 1. Preliminaries 2
1.1. Basic notation 3
1.2. Morphisms associated to line bundles; ample line bundles 4
1.3. Riemann - Roch and Hodge Index theorems 5
Part 2. Mori theory for surfaces 6
2.1. Mori-Kleiman cone 6
2.2. Examples 9
2.3. The rationality lemma and the cone theorem 11
2.4. Castelnuovo contraction theorem 16
2.5. Base point freeness, BPF 16
2.6. Minimal model program for surfaces 20
Part 3. Birational theory for surfaces 22
3.1. Castelnuovo rationality criterium 22
3.2. Factorization of birational morphisms 23
3.3. Singularities and log singularities. 25

Source: Andreatta, Marco - Dipartimento di Matematica, Università di Trento

Collections: Mathematics