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arXiv · 2606.31224

Nowhere-vanishing harmonic 1-forms on real loci of K3-fibred Calabi-Yau 3-folds

Shih-Kai Chiu·Daniel Platt·Calum Spicer
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Abstract

We develop an analytic construction of nowhere-vanishing harmonic $1$-forms on real loci of K3-fibred Calabi-Yau $3$-folds with collapsing Ricci-flat K\"ahler metrics. We apply our construction to examples whose real loci have connected components diffeomorphic to $S^1\times S^2$ and to both trivial and nontrivial mapping tori. As an application, we produce examples of compact $7$-manifold with holonomy $G_2$ via the Joyce-Karigiannis construction.

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Shih-Kai Chiu, Daniel Platt, Calum Spicer. 2026-06-30. Nowhere-vanishing harmonic 1-forms on real loci of K3-fibred Calabi-Yau 3-folds. https://arxiv.org/abs/2606.31224

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