Weight functions on Berkovich curves

Matthew Baker; Johannes Nicaise

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arXiv · 1506.01263

Weight functions on Berkovich curves

Matthew Baker·Johannes Nicaise

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Abstract

Let $C$ be a curve over a complete discretely valued field $K$. We give tropical descriptions of the weight function attached to a pluricanonical form on $C$ and the essential skeleton of $C$. We show that the Laplacian of the weight function equals the pluricanonical divisor on Berkovich skeleta, and we describe the essential skeleton of $C$ as a combinatorial skeleton of the Berkovich skeleton of the minimal $snc$-model. In particular, if $C$ has semi-stable reduction, then the essential skeleton coincides with the minimal skeleton. As an intermediate step, we describe the base loci of logarithmic pluricanonical line bundles on minimal $snc$-models.

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BibTeX RIS

Matthew Baker, Johannes Nicaise. 2015-10-28. Weight functions on Berkovich curves. https://arxiv.org/abs/1506.01263

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