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arXiv · 2406.18092

Polarized endomorphisms of log Calabi-Yau pairs

Joaquín Moraga·José Ignacio Yáñez·Wern Yeong
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Abstract

Let $(X,\Delta)$ be a dlt log Calabi-Yau pair admitting a polarized endomorphism. We show that $(X,\Delta)$ is a finite quotient of a toric log Calabi-Yau fibration over an abelian variety. We provide an example which shows that the previous statement does not hold if we drop the dlt condition of $(X,\Delta)$ even if $X$ is a smooth variety. Given a klt type variety $X$ and a log Calabi-Yau pair $(X,\Delta)$ admitting a polarized endomorphism, we show that a suitable birational modification of $(X,\Delta)$ is a finite quotient of a toric log Calabi-Yau fibration over an abelian variety.

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Joaquín Moraga, José Ignacio Yáñez, Wern Yeong. 2024-06-26. Polarized endomorphisms of log Calabi-Yau pairs. https://arxiv.org/abs/2406.18092

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