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2016 Weight functions on Berkovich curves
Matthew Baker, Johannes Nicaise
Algebra Number Theory 10(10): 2053-2079 (2016). DOI: 10.2140/ant.2016.10.2053

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 semistable 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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Matthew Baker. Johannes Nicaise. "Weight functions on Berkovich curves." Algebra Number Theory 10 (10) 2053 - 2079, 2016. https://doi.org/10.2140/ant.2016.10.2053

Information

Received: 28 October 2015; Revised: 24 June 2016; Accepted: 2 October 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1375.14208
MathSciNet: MR3582013
Digital Object Identifier: 10.2140/ant.2016.10.2053

Subjects:
Primary: 14D10
Secondary: 14E30, 14T05

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.10 • No. 10 • 2016
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