Basepoint freeness for nef and big line bundles in positive characteristic

• 成果类型: Article
• 署名作者: Keel, S
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/121025
• 发表日期: 1999
• 页码: 253-286
• 关键词: moduli spaces; intersection theory; pointed curves; projectivity; threefolds

摘要

A necessary and sufficient condition is given for semi-ampleness of a numerically effective (nef) and big line bundle in positive characteristic. One application is to the geometry of the universal stable curve over (M) over bar(g), specifically, the semi-ampleness of the relative dualizing sheaf, ill positive characteristic. An example is given which shows this and the semi-ampleness criterion fail in characteristic zero. A second application is to Mori's program for minimal models of 3-folds in positive characteristic, namely, to the existence of birational extremal contractions.