✦ LIBER ✦
Stable Limits of Log Surfaces and Cohen–Macaulay Singularities
✍ Scribed by Brendan Hassett
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 103 KB
- Volume
- 242
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
Given a family of surfaces of general type over a smooth curve, one can apply semistable reduction and the minimal model program to obtain a stable reduction. This is the basis for a geometric compactification for moduli spaces of surfaces of general type, due to Kollár, Shepherd-Barron, and Alexeev. However, this approach hinges on the fact that the resulting stable limit has relatively mild singularities; in particular, it should be Cohen-Macaulay. Unfortunately, the standard formalism does not guarantee that stable limits of families of log surfaces are Cohen-Macaulay.
Here we prove that this is the case.