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

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arxiv 1907.09780 v3 pith:FVFMTRGN submitted 2019-07-23 math.DG math.APmath.CV

Takahiro Aoi This is my paper · ORCID
classification math.DGmath.APmath.CV
keywords hlermetricscalar-flataffinealgebraicassumptioncompleteconstant
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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 K\"{a}hler metric on $X \setminus D$ on the assumption that $D$ has a constant positive scalar curvature K\"{a}hler metric.

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  1. Almost scalar-flat K\"{a}hler metrics on affine algebraic manifolds

    math.DG 2019-08 conditional novelty 6.0 of 10

    Complete almost scalar-flat Kähler metrics exist on X\D when K_X^{-l}⊗L_X^m is very ample and m/l is sufficiently small relative to the average scalar curvature of D.

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