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arXiv · 2304.03163

Compact K\"ahler three-folds with nef anti-canonical bundle

Shin-ichi Matsumura·Xiaojun Wu
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Abstract

In this paper, we prove that a non-projective compact K\"ahler three-fold with nef anti-canonical bundle is, up to a finite \'etale cover, one of the following: a manifold with vanishing first Chern class; the product of a K3 surface and the projective line; or a projective space bundle over a $2$-dimensional torus. This result extends Cao-H\"oring's structure theorem for projective manifolds to compact K\"ahler manifolds in dimension $3$. For the proof, we investigate the Minimal Model Program for compact K\"ahler three-folds with nef anti-canonical bundles by using the positivity of direct image sheaves, $\mathbb{Q}$-conic bundles, and orbifold vector bundles.

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Shin-ichi Matsumura, Xiaojun Wu. 2023-02-24. Compact K\"ahler three-folds with nef anti-canonical bundle. https://doi.org/10.1007/s00208-024-02934-5

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