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arXiv · 2012.04496

Invariant scalar-flat K\"ahler metrics on line bundles over generalized flag varieties

Qi Yao
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Abstract

Let $G$ be a simply-connected semisimple compact Lie group, $X$ a compact K\"ahler manifold homogeneous under $G$, and $L$ a negative $G$-equivariant holomorphic line bundle over $X$. We prove that all $G$-invariant K\"ahler metrics on the total space of $L$ arise from the Calabi ansatz. Using this, we then show that there exists a unique $G$-invariant scalar-flat K\"ahler metric in each K\"ahler class of $L$.

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Qi Yao. 2020-12-08. Invariant scalar-flat K\"ahler metrics on line bundles over generalized flag varieties. https://doi.org/10.4153/s0008414x24000464

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