Deformations of extremal toric manifolds

Details Deformations of extremal toric manifolds Deformations of extremal toric manifolds

2012-01-19

arxiv.org/abs/1201.4137v2

Mathematics

Differential Geometry

29 pages, 9 figures Some minor mistakes and terminology corrected

Scientific paper

Let $X$ be a compact toric extremal K\"ahler manifold. Using the work of
Sz\'ekelyhidi, we provide a simple criterion on the fan describing $X$ to
ensure the existence of complex deformations of $X$ that carry extremal
metrics. As an example, we find new CSC metrics on 4-points blow-ups of
$\C\P^1\times\C\P^1$.

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