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

Jiangtao Li

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arXiv · 2505.14006

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

Jiangtao Li

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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]).

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Jiangtao Li. 2025-05-20. Finite generation of the ring of holomorphic functions with polynomial growth on the Kähler-Ricci shrinker. https://arxiv.org/abs/2505.14006

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