Work

Dimension Estimate and Existence of Holomorphic Sections With Polynomial Growth on Gradient Kähler Ricci Shrinkers

Year: 2025

Type: article

Abstract: In this paper, we show that the dimension for the space of holomorphic $(p, 0)$-forms and holomorphic sections of the pluri-anticanonical line bundle $K_{M}^{-q}$ with polynomial growth on gradient Kähler–Ricci shrinkers with bounded curvature is bounded from above by a power function of the growth rate. We also prove the existence of holomorphic sections of $K_{M}^{-q}$ with polynomial growth when the Kähler–Ricci shrinker is asymptotically conical, provided $q$ is sufficiently large. As an application, we show that the Kodaira map constructed using such sections is a holomorphic embedding into a complex projective space.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaf350

Authors: Fei He, Jianyu Ou

Institution: Xiamen University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G4952392286, G6194665756, G8532141224