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2016 The greatest Ricci lower bound, conical Einstein metrics and Chern number inequality
Jian Song, Xiaowei Wang
Geom. Topol. 20(1): 49-102 (2016). DOI: 10.2140/gt.2016.20.49

Abstract

We partially confirm a conjecture of Donaldson relating the greatest Ricci lower bound R(X) to the existence of conical Kähler–Einstein metrics on a Fano manifold X. In particular, if D | KX| is a smooth divisor and the Mabuchi K–energy is bounded below, then there exists a unique conical Kähler–Einstein metric satisfying Ric(g) = βg + (1 β)[D] for any β (0,1). We also construct unique conical toric Kähler–Einstein metrics with β = R(X) and a unique effective –divisor D [KX] for all toric Fano manifolds. Finally we prove a Miyaoka–Yau-type inequality for Fano manifolds with R(X) = 1.

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Jian Song. Xiaowei Wang. "The greatest Ricci lower bound, conical Einstein metrics and Chern number inequality." Geom. Topol. 20 (1) 49 - 102, 2016. https://doi.org/10.2140/gt.2016.20.49

Information

Received: 5 December 2013; Revised: 16 April 2015; Accepted: 9 June 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1342.32018
MathSciNet: MR3470713
Digital Object Identifier: 10.2140/gt.2016.20.49

Subjects:
Primary: 32Q20, 53C55

Rights: Copyright © 2016 Mathematical Sciences Publishers

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