Complete scalar-flat K\"{a}hler metrics on certain affine algebraic manifold
アブストラクト
In 1990, Bando-Kobayashi showed that if a smooth hypersurface in a Fano manifold has a Ricci-positive K\"{a}hler Einstein metric, then its complement admits a complete Ricci-flat K\"{a}hler metric.
In this talk, I will talk about a scalar curvature version of this result.
Namely, I will explain the recent result on the existence of a complete scalar-flat K\"{a}hler metric on a complement of a constant positive scalar curvature K\"{a}hler smooth hypersurface in polarized manifold.