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arXiv · 1201.4137

Deformations of extremal toric manifolds

Yann Rollin·Carl Tipler
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Abstract

Let $X$ be a compact toric extremal K\"ahler manifold. Using the work of Sz\'ekelyhidi, 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 $\C\P^1\times\C\P^1$.

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Yann Rollin, Carl Tipler. 2012-01-19. Deformations of extremal toric manifolds. https://doi.org/10.1007/s12220-013-9403-z

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