Cambridge University Press eBooks· 2013
Singularities of the Minimal Model Program
- 672citations
- 2013year
Short summary
This book presents a comprehensive and self-contained theory of singularities arising in the Minimal Model Program (MMP) and moduli problems for algebraic varieties, including new unpublished results.
AI-generated from the title and abstract; the full text is not read.
Key points
- Provides a comprehensive theory of singularities relevant to the Minimal Model Program (MMP).
- Details the intertwined development of singularity theory and Mori's program.
- Covers terminal, canonical, and log canonical singularities, linking them to the abundance conjecture.
- Includes previously unpublished results, offering new insights.
AI-generated from the title and abstract; the full text is not read.
Abstract
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interwoven threads, presenting a self-contained and complete theory of these singularities, including many previously unpublished results.
The authors' abstract, as published at the source. Cambridge University Press eBooks, 2013 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Geometry and Topology
Geometry and TopologyMathematics