Coupled K\"ahler-Ricci solitons on toric Fano manifolds
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Publication:6294452
DOI10.2140/APDE.2019.12.2067arXiv1711.09881MaRDI QIDQ6294452
Publication date: 27 November 2017
Abstract: We prove a necessary and sufficient condition in terms of the barycenters of a collection of polytopes for existence of coupled K"ahler-Einstein metrics on toric Fano manifolds. This confirms the toric case of a coupled version of the Yau-Tian-Donaldson conjecture. We also obtain a necessary and sufficient condition for existence of torus-invariant solutions to a system of soliton type equations on toric Fano manifolds. Some of these solutions provide natural candidates for the large time limits of a certain geometric flow generalizing the K"ahler-Ricci flow.
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