Let be a curve over a complete discretely valued field . We give tropical descriptions of the weight function attached to a pluricanonical form on and the essential skeleton of . We show that the Laplacian of the weight function equals the pluricanonical divisor on Berkovich skeleta, and we describe the essential skeleton of as a combinatorial skeleton of the Berkovich skeleton of the minimal snc-model. In particular, if 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.
"Weight functions on Berkovich curves." Algebra Number Theory 10 (10) 2053 - 2079, 2016. https://doi.org/10.2140/ant.2016.10.2053