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arXiv · 2602.20488

Families of projective bundles that admit coupled K\"ahler-Einstein metrics but no K\"ahler-Einstein metrics

Naoto Yotsutani
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Abstract

We construct two families of projective bundles that admit two-coupled K\"ahler-Einstein (cKE) metrics but do not ordinary K\"ahler-Einstein metrics in sufficiently high dimensions. We also prove that no such examples arise among toric Fano threefolds, for any decomposition of $c_1(X)$, when considering the natural projection onto $\mathbb P^1$.

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Naoto Yotsutani. 2026-02-24. Families of projective bundles that admit coupled K\"ahler-Einstein metrics but no K\"ahler-Einstein metrics. https://arxiv.org/abs/2602.20488

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