Almost 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 show the existence of a complete Kähler metric on $X\setminus D$ whose scalar curvature is flat away from some divisor if there are positive integers $l(>n),m$ such that the line bundle $K_X^{-l}\otimes L_X^m$ is very ample and the ratio $m/l$ is sufficiently small.

arXiv comment24 pages, no figures, This paper is merged with arXiv:1907.09780 and arXiv:1910.12317 and appear in Math. Z

References in corpus (1)

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