Finite generation of the ring of holomorphic functions with polynomial growth on the Kähler-Ricci shrinker

2025/05/20 by Li, Jiangtao
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.14006

Abstract

Let (X, g, J, f ) be a non-compact gradient shrinking Kahler-Ricci soliton. We prove that if the scalar curvature of X satisfies a mild assumption, then OP (X), the ring of holomorphic functions with polynomial growth on X, is finitely generated. This gives a partial confirmation to a conjecture of Munteanu and Wang (cf.[MW14]).

Citations

• A new complete two-dimensional shrinking gradient Kähler-Ricci soliton
• Singularities of linear systems and boundedness of Fano varieties
• Sharp Dimension Estimates of Holomorphic Functions and Rigidity

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• Uniqueness of shrinking Kähler-Ricci solitons on resolutions of Kähler cones
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• A note on the uniformization of gradient Kähler-Ricci solitons