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arXiv · 1711.08424

Extremal Kähler Poincaré type metrics on toric varieties

Vestislav Apostolov·Hugues Auvray·Lars Martin Sektnan
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Abstract

We develop a general theory for the existence of extremal Kähler metrics of Poincaré type in the sense of Auvray, defined on the complement of a toric divisor of a polarized toric variety. In the case when the divisor is smooth, we obtain a list of necessary conditions which must be satisfied for such a metric to exist. Using the explicit methods of Apostolov-Calderbank-Gauduchon together with the computational approach of Sektnan, we show that on a Hirzebruch complex surface the necessary conditions are also sufficient. In particular, on such a complex surface the complement of the infinity section admits an extremal Kähler metric of Poincaré type whereas the complement of a fibre admits a complete ambitoric extremal Kähler metric which is not of Poincaré type.

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BibTeXRIS

Vestislav Apostolov, Hugues Auvray, Lars Martin Sektnan. 2017-11-22. Extremal Kähler Poincaré type metrics on toric varieties. https://arxiv.org/abs/1711.08424

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