Geometry & Topology
- Geom. Topol.
- Volume 20, Number 1 (2016), 49-102.
The greatest Ricci lower bound, conical Einstein metrics and Chern number inequality
We partially confirm a conjecture of Donaldson relating the greatest Ricci lower bound to the existence of conical Kähler–Einstein metrics on a Fano manifold . In particular, if is a smooth divisor and the Mabuchi –energy is bounded below, then there exists a unique conical Kähler–Einstein metric satisfying for any . We also construct unique conical toric Kähler–Einstein metrics with and a unique effective –divisor for all toric Fano manifolds. Finally we prove a Miyaoka–Yau-type inequality for Fano manifolds with .
Geom. Topol., Volume 20, Number 1 (2016), 49-102.
Received: 5 December 2013
Revised: 16 April 2015
Accepted: 9 June 2015
First available in Project Euclid: 16 November 2017
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Song, Jian; Wang, Xiaowei. The greatest Ricci lower bound, conical Einstein metrics and Chern number inequality. Geom. Topol. 20 (2016), no. 1, 49--102. doi:10.2140/gt.2016.20.49. https://projecteuclid.org/euclid.gt/1510858923