E-Book Overview
A large part of this book is a digest of the great work of Shokurov [Sho03]: in particular, we give a complete and essentially self-contained construction of 3-fold and 4-fold kit flips.Shokurov has introduced many new ideas in the field and has made huge progress on the construction of higher dimensional flips. However. [Sho03] is very difficult to understand: in this book, we rewrite the entire subject from scratch.
E-Book Content
Flips for 3-folds and 4-folds Florin Ambro Res. Inst. Math. Sci., Kyoto University Kyoto 606-8502, Japan Alessio Corti Department of Mathematics, Imperial College London Huxley Building, 180 Queen’s Gate London SW7 2AZ, UK Osamu Fujino Grad. School of Math., Nagoya University Chikusa-ku, Nagoya 464-8602, Japan Christopher D. Hacon Department of Mathematics, University of Utah 155 South 1400 East Salt Lake City UT 84112-0090, USA J´anos Koll´ar Department of Mathematics, Princeton University Fine Hall, Washington Road Princeton NJ 08544-1000, USA James Mc Kernan Department of Mathematics, UC Santa Barbara Santa Barbara CA 93106, USA Hiromichi Takagi Grad. School of Math. Sci., The University of Tokyo 3-8-1 Komaba, Meguro-ku, Tokyo 153–8914, Japan
Contents Chapter 1. Introduction Alessio Corti 1.1. Minimal models of surfaces 1.2. Higher dimensions and flips 1.3. The work of Shokurov 1.4. Minimal models of 3-folds and 4-folds 1.5. The aim of this book 1.6. Pl flips 1.7. b-divisors 1.8. Restriction and mobile b-divisors. 1.9. Pbd-algebras 1.10. Restricted systems and 3-fold pl flips 1.11. Shokurov’s finite generation conjecture 1.12. What is log terminal? 1.13. Special termination and reduction to pl flips. 1.14. The work of Hacon and Mc Kernan: adjoint algebras 1.15. Mobile b-divisors on weak klt del Pezzo surfaces 1.16. The CCS Conjecture 1.17. Kodaira’s canonical bundle formula and subadjunction 1.18. Finite generation on non-klt surface