Vol. 100, No. 2 DUKE MATHEMATICAL JOURNAL © 1999 ON THE FUTAKI INVARIANTS OF COMPLETE INTERSECTIONS

Abstract

obstruction of Kazdan-Warner to prescribe Gauss curvature on S 2. The Futaki invariants are defined for any compact Kähler manifold with positive first Chern class that has nontrivial holomorphic vector fields. Their vanishing is a necessary condition to the existence of Kähler-Einstein metrics on the underlying manifold