摘要翻译:
应用Nadel乘子理想束的方法,证明了自同构群无不动点作用的最多6次的复del Pezzo曲面具有K\\“Ahler-Einstein度量,特别地,证明了所有4,5,6$次的del Pezzo曲面和某些特殊的低次del Pezzo曲面具有K\\”Ahler-Einstein度量。这个结果并不是新的,但本文给出的证明比Siu、Tian和Tian-Yau的早期证明涉及更少。
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英文标题:
《Existence of K\"ahler-Einstein metrics and multiplier ideal sheaves on
del Pezzo surfaces》
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作者:
Gordon Heier
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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一级分类:Mathematics 数学
二级分类:Complex Variables 复变数
分类描述:Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数,自守群作用与形式,伪凸性,复几何,解析空间,解析束
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一级分类:Mathematics 数学
二级分类:Differential Geometry 微分几何
分类描述:Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis
复形,接触,黎曼,伪黎曼和Finsler几何,相对论,规范理论,整体分析
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英文摘要:
We apply Nadel's method of multiplier ideal sheaves to show that every complex del Pezzo surface of degree at most six whose automorphism group acts without fixed points has a K\"ahler-Einstein metric. In particular, all del Pezzo surfaces of degree $4,5$, or $6$ and certain special del Pezzo surfaces of lower degree are shown to have a K\"ahler-Einstein metric. This result is not new, but the proofs given in the present paper are less involved than earlier ones by Siu, Tian and Tian-Yau.
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PDF链接:
https://arxiv.org/pdf/0710.5724