Abstract
In this note we report on examples of 7- and 8-dimensional toric Fano manifolds whose associated reflexive polytopes are not symmetric, but they still admit a Kahler–Einstein metric. This answers a question first posed by Batyrev and Selivanova. The examples were found in the classification of ≤8-dimensional toric Fano manifolds obtained by Obro. We also discuss related open questions and conjectures. In particular, we notice that the alpha-invariants of these examples do not satisfy the assumptions of Tian’s theorem.
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