Singularities of the Minimal Model Program
Seiten
2013
Cambridge University Press (Verlag)
978-1-107-03534-8 (ISBN)
Cambridge University Press (Verlag)
978-1-107-03534-8 (ISBN)
Giving a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties, this book will become a standard reference for anyone interested in higher-dimensional questions in algebraic geometry, analytic geometry and number theory.
This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study of these singularities and the development of Mori's program have been deeply intertwined. Early work on minimal models relied on detailed study of terminal and canonical singularities but many later results on log terminal singularities were obtained as consequences of the minimal model program. Recent work on the abundance conjecture and on moduli of varieties of general type relies on subtle properties of log canonical singularities and conversely, the sharpest theorems about these singularities use newly developed special cases of the abundance problem. This book untangles these interwoven threads, presenting a self-contained and complete theory of these singularities, including many previously unpublished results.
This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study of these singularities and the development of Mori's program have been deeply intertwined. Early work on minimal models relied on detailed study of terminal and canonical singularities but many later results on log terminal singularities were obtained as consequences of the minimal model program. Recent work on the abundance conjecture and on moduli of varieties of general type relies on subtle properties of log canonical singularities and conversely, the sharpest theorems about these singularities use newly developed special cases of the abundance problem. This book untangles these interwoven threads, presenting a self-contained and complete theory of these singularities, including many previously unpublished results.
János Kollár is Professor of Mathematics and Donner Professor of Science at Princeton University. He has authored about 100 research papers and six books on algebraic geometry.
Preface; Introduction; 1. Preliminaries; 2. Canonical and log canonical singularities; 3. Examples; 4. Adjunction and residues; 5. Semi-log-canonical pairs; 6. Du Bois property; 7. Log centers and depth; 8. Survey of further results and applications; 9. Finite equivalence relations; 10. Appendices; References; Index.
| Reihe/Serie | Cambridge Tracts in Mathematics |
|---|---|
| Co-Autor | Sándor Kovács |
| Zusatzinfo | Worked examples or Exercises; 45 Tables, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 157 x 231 mm |
| Gewicht | 660 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-107-03534-1 / 1107035341 |
| ISBN-13 | 978-1-107-03534-8 / 9781107035348 |
| Zustand | Neuware |
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