Toward a construction of scalar-flat Kähler metrics on affine algebraic manifolds

Abstract

Let $(X,L_X)$ be an $n$-dimensional polarized manifold. Let $D$ be a smooth hypersurface defined by a holomorphic section of $L_X$. In this paper, we study the existence of a complete scalar-flat Kähler metric on $X\setminus D$ on the assumption that $D$ has a constant positive scalar curvature Kähler metric.

arXiv comment28 pages, no figures, This paper is merged with arXiv:1908.05583 and arXiv:1910.12317 and appear in Math. Z

References in corpus (1)

• Regularity properties of the degenerate Monge--Ampère equations compact Kähler manifolds