# Toward a construction of scalar-flat K\"{a}hler metrics on affine algebraic manifolds

Research paper by Takahiro Aoi

Indexed on: 24 Jun '20Published on: 23 Jul '19Published in: arXiv - Mathematics - Differential Geometry

#### Abstract

In this paper, we study the existence of a complete {\kah} metric which has a flat scalar curvature on the complement of the smooth hypersurface $D$ with a constant positive scalar curvature {\kah} metric on some polarized manifold without nonzero holomorphic vector field vanishing on $D$.