摘要翻译:
研究了向量丛截面完全交上常标量曲率Kaehler度量的存在性问题。特别地,我们给出了这样一个流形的Futaki不变量与定义它的截面的权重以及环境流形的Futaki不变量之间的一般公式。作为应用,我们给出了Fano五重不承认Kaehler-Einstein度量的Mukai-Umemura-Tian样例,以及Grassmannian上完全交的K-稳定性的有力证据。
---
英文标题:
《On the K-stability of complete intersections in polarized manifolds》
---
作者:
Claudio Arezzo, Alberto Della Vedova
---
最新提交年份:
2008
---
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
--
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
--
---
英文摘要:
We consider the problem of existence of constant scalar curvature Kaehler metrics on complete intersections of sections of vector bundles. In particular we give general formulas relating the Futaki invariant of such a manifold to the weight of sections defining it and to the Futaki invariant of the ambient manifold. As applications we give a new Mukai-Umemura-Tian like example of Fano 5-fold admitting no Kaehler-Einstein metric and a strong evidence of K-stability of complete intersections on Grassmannians.
---
PDF链接:
https://arxiv.org/pdf/0810.1473