A Fixed Point Formula for $0$-pseudofree $S^1$-actions on K\"ahler Manifolds of Constant Scalar Curvature

Abstract

Let $M$ be an $m$-dimensional compact complex manifold and $\Omega$ a Kähler class of $M$. Assume that $M$ admits an $\Omega$-preserving $0$-pseudofree $S^1$-action and that $\Omega$ contains a Kähler metric of constant scalar curvature. Then using the fixed point formula for the Bando-Calabi-Futaki character obtained in [5], we can obtain information on the fixed point data of the $S^1$-action. Our main result is Theorem 2.