Differential forms on log canonical spaces
Differential forms on log canonical spaces
复制标题
对数正则空间上的微分形式
DOI：
10.1007/s10240-011-0036-0
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
T. Peternell
中科院分区：
文献类型：
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作者：
D. Greb;Stefan Kebekus;Sandor J. Kovacs;T. Peternell
本文研究对数标准簇上的微分形式。它表明，任何p-形式上定义的光滑轨迹的各种典型或klt奇点定期扩展到任何决议的奇点。事实上，对数典型对的一个更一般的定理被建立。证明依赖于消失定理的日志典型品种和方法的最小模型计划。此外，发展了dlt对的微分形式理论。它表明，许多已知的基本定理和技术层的对数微分光滑品种也持有dlt setting.Immediate应用程序包括存在的拉回映射的自反微分，推广的Bogomolov-Sommese型消失的结果，并积极回答Lipman-Zerkki猜想的klt空间。
The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities. In fact, a much more general theorem for log canonical pairs is established. The proof relies on vanishing theorems for log canonical varieties and on methods of the minimal model program. In addition, a theory of differential forms on dlt pairs is developed. It is shown that many of the fundamental theorems and techniques known for sheaves of logarithmic differentials on smooth varieties also hold in the dlt setting.Immediate applications include the existence of a pull-back map for reflexive differentials, generalisations of Bogomolov-Sommese type vanishing results, and a positive answer to the Lipman-Zariski conjecture for klt spaces.