Convergence of cscK metrics on smooth minimal models of general type

Wanxing Liu

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arXiv · 2012.09934

Convergence of cscK metrics on smooth minimal models of general type

Wanxing Liu

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Abstract

We consider constant scalar curvature K\"{a}hler metrics on a smooth minimal model of general type in a neighborhood of the canonical class, which is the perturbation of the canonical class by a fixed K\"{a}hler metric. We show that sequences of such metrics converge smoothly on compact subsets away from a subvariety to the singular K\"{a}hler Einstein metric in the canonical class. This confirms partially a conjecture of Jian-Shi-Song about the convergence behavior of such sequences.

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Wanxing Liu. 2020-12-17. Convergence of cscK metrics on smooth minimal models of general type. https://arxiv.org/abs/2012.09934

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