Gromov-Hausdorff Limits of Kähler Manifolds with Ricci Curvature Bounded Below II

Gang Liu; Gábor Szekelyhidi

doi:10.1002/cpa.21900

Gromov-Hausdorff Limits of Kähler Manifolds with Ricci Curvature Bounded Below II

Gang Liu, Gábor Szekelyhidi

School of Mathematical Sciences

University of Notre Dame

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We study noncollapsed Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below. Our main result is that each tangent cone is homeomorphic to a normal affine variety. This extends a result of Donaldson-Sun, who considered noncollapsed limits of polarized Kähler manifolds with two-sided Ricci curvature bounds.

Original language	English
Pages (from-to)	909-931
Number of pages	23
Journal	Communications on Pure and Applied Mathematics
Volume	74
Issue number	5
DOIs	https://doi.org/10.1002/cpa.21900
State	Published - May 2021

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title = "Gromov-Hausdorff Limits of K{\"a}hler Manifolds with Ricci Curvature Bounded Below II",

abstract = "We study noncollapsed Gromov-Hausdorff limits of K{\"a}hler manifolds with Ricci curvature bounded below. Our main result is that each tangent cone is homeomorphic to a normal affine variety. This extends a result of Donaldson-Sun, who considered noncollapsed limits of polarized K{\"a}hler manifolds with two-sided Ricci curvature bounds.",

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AU - Liu, Gang

AU - Szekelyhidi, Gábor

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N2 - We study noncollapsed Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below. Our main result is that each tangent cone is homeomorphic to a normal affine variety. This extends a result of Donaldson-Sun, who considered noncollapsed limits of polarized Kähler manifolds with two-sided Ricci curvature bounds.

AB - We study noncollapsed Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below. Our main result is that each tangent cone is homeomorphic to a normal affine variety. This extends a result of Donaldson-Sun, who considered noncollapsed limits of polarized Kähler manifolds with two-sided Ricci curvature bounds.

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JO - Communications on Pure and Applied Mathematics

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Gromov-Hausdorff Limits of Kähler Manifolds with Ricci Curvature Bounded Below II

Abstract

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