Geometry and Topology of the space of Kähler metrics on singular varieties

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Title: Geometry and Topology of the space of Kähler metrics on singular varieties
Authors: Nezza, ED
Guedj, V
Item Type: Working Paper
Abstract: Let $Y$ be a compact K\"ahler normal space and $\alpha \in H^{1,1}(Y,\mathbb{R})$ a K\"ahler class. We study metric properties of the space $\mathcal{H}_\alpha$ of K\"ahler metrics in $\alpha$ using Mabuchi geodesics. We extend several results by Calabi, Chen, Darvas previously established when the underlying space is smooth. As an application we analytically characterize the existence of K\"ahler-Einstein metrics on $\mathbb{Q}$-Fano varieties, generalizing a result of Tian, and illustrate these concepts in the case of toric varieties.
Issue Date: 31-Aug-2018
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: Marie Skłodowska-Curie Action 660940 — KRF-CY (MSCA–IF)
Keywords: math.DG
Notes: 44 pages. arXiv admin note: substantial text overlap with arXiv:1401.7857. v2: Section 1 and the statement of Theorem B have been modified
Appears in Collections:Faculty of Natural Sciences

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