ON THE MODIFIED FUTAKI INVARIANT OF COMPLETE INTERSECTIONS IN PROJECTIVE SPACES
ON THE MODIFIED FUTAKI INVARIANT OF COMPLETE INTERSECTIONS IN PROJECTIVE SPACES
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DOI：
10.1017/nmj.2016.16
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发表时间：
2014-10
影响因子：
0.8
通讯作者：
Ryosuke Takahashi
中科院分区：
文献类型：
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作者：
Ryosuke Takahashi
设M是一个Fano流形。我们称c_{1}（M）$中的Kähler度量${\it\omega}为Kähler-Ricci孤子，如果它满足方程$\text{Ric}（{\it\omega}）-{\it\omega}=L_{V}{\it\omega}$，其中V$是M$上的全纯向量场。已知Kähler-Ricci孤子存在的一个必要条件是由Tian和Zhu引入的修正的Futaki不变量为零。在Berman和Nyström最近的工作中，它被推广到（可能是奇异的）Fano簇，并引入了对$（M，V）$的代数几何稳定性的概念。本文提出了一种计算射影空间中Fano完全交的修正Futaki不变量的方法。
Let $M$ be a Fano manifold. We call a Kähler metric ${\it\omega}\in c_{1}(M)$ a Kähler–Ricci soliton if it satisfies the equation $\text{Ric}({\it\omega})-{\it\omega}=L_{V}{\it\omega}$ for some holomorphic vector field $V$ on $M$. It is known that a necessary condition for the existence of Kähler–Ricci solitons is the vanishing of the modified Futaki invariant introduced by Tian and Zhu. In a recent work of Berman and Nyström, it was generalized for (possibly singular) Fano varieties, and the notion of algebrogeometric stability of the pair $(M,V)$ was introduced. In this paper, we propose a method of computing the modified Futaki invariant for Fano complete intersections in projective spaces.