Deformations of extremal toric manifolds

Abstract

Let $X$ be a compact toric extremal Kähler manifold. Using the work of Székelyhidi, we provide a combinatorial 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 $\C¶^1\times\C¶^1$.

25 pages, 9 figures, final version, to appear in JGA

Cited by in corpus (3)

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• Deformations of Smooth Complete Toric Varieties: Obstructions and the Cup Product
• Foldable fans, cscK surfaces and local K-moduli