Examples of non-symmetric Kähler-Einstein toric Fano manifolds

Details Examples of non-symmetric Kähler-Einstein toric Fano manifolds Examples of non-symmetric Kähler-Einstein toric Fano manifolds

2009-05-13

arxiv.org/abs/0905.2054v2

Mathematics

Algebraic Geometry

AMS-LaTeX, 8 pages; final version (references updated)

Scientific paper

In this note we report on examples of 7- and 8-dimensional toric Fano manifolds that are not symmetric and still admit a Kaehler-Einstein metric. This answers a question first posed by V.V. Batyrev and E. Selivanova. The examples were found in the classification of toric Fano manifolds up to dimension 8 obtained by M. Oebro. We also discuss related open questions and conjectures.

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