Compact Moduli Spaces of Del Pezzo Surfaces and K\"ahler-Einstein metrics
Compact Moduli Spaces of Del Pezzo Surfaces and K\"ahler-Einstein metrics
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DOI：
10.4310/jdg/1452002879
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发表时间：
2012-10
期刊：
影响因子：
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通讯作者：
Y. Odaka;Cristiano Spotti;Song Sun
中科院分区：
文献类型：
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作者：
Y. Odaka;Cristiano Spotti;Song Sun
我们证明了Kahler-Einstein Del Pezzo曲面模空间的Gromov-Hausdorff紧化在每一度上都与一定的代数几何紧化一致。特别是，这恢复田的定理存在的Kahler-Einstein度量光滑Del Pezzo表面和分类退化等度量。证明是基于代数和微分几何技术的组合。
We prove that the Gromov-Hausdorff compactification of the moduli space of Kahler-Einstein Del Pezzo surfaces in each degree agrees with certain algebro-geometric compactification. In particular, this recovers Tian's theorem on the existence of Kahler-Einstein metrics on smooth Del Pezzo surfaces and classifies the degenerations of such metrics. The proof is based on a combination of both algebraic and differential geometric techniques.