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arXiv · 2608.08665

The Fino--Vezzoni conjecture on homogeneous spaces

Joseph Kwong
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Abstract

We prove that a compact discrete quotient of a complex homogeneous space with compact isotropy is K\"ahler whenever it admits both a balanced metric and a pluriclosed metric. Moreover, if its real first Chern class vanishes, then the pluriclosed flow starting from any invariant pluriclosed metric exists for all time and converges smoothly to a flat K\"ahler metric.

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Joseph Kwong. 2026-08-09. The Fino--Vezzoni conjecture on homogeneous spaces. https://arxiv.org/abs/2608.08665

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