It is known that a necessary condition for the existence of K\"ahler-Riccisolitons is the vanishing of the modified Futaki invariant introduced byTian-Zhu. In a recent work of Berman-Nystr\"om, it was generalized for(singular) Fano varieties and the notion of algebro-geometric stability of thepair $(M,V)$ of a Fano manifold $M$ and a holomorphic vector field $V$ wasintroduced. In this paper, we propose a method of computing the modified Futakiinvariant for Fano complete intersections in projective spaces.
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机译：众所周知，存在K'ahler-Riccisolitons的必要条件是由Tian-Zhu引入的修改后的Futaki不变量的消失。在Berman-Nystr'om的最新著作中，它被推广为（奇异的）Fano引入了Fano流形$ M $对和纯全矢量场$ V $对的（$，M，V）$的代数几何稳定性的概念。在本文中，我们提出了一种计算投影空间中Fano完整相交的修正Futaki不变量的方法。
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