A note on the transcendental basepoint-free conjecture for Calabi-Yau manifolds

Bastien Philippe

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arXiv · 2606.30046

A note on the transcendental basepoint-free conjecture for Calabi-Yau manifolds

Bastien Philippe

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Abstract

In this note, we prove that the transcendental basepoint-free conjecture for Calabi-Yau manifolds holds if it holds for its hyperk{\"a}hler factors in its Beauville-Bogomolov decomposition. Based on a contraction theorem due to Bakker and Lehn, we show that the conjecture holds for a big and nef class $\alpha$ on a hyperk{\"a}hler manifold under a mild condition on the dimension of the space generated by classes of rational curves on which $\alpha$ vanishes.

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Bastien Philippe. 2026-06-29. A note on the transcendental basepoint-free conjecture for Calabi-Yau manifolds. https://arxiv.org/abs/2606.30046

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