# Essential skeletons of pairs and the geometric P=W conjecture.

@article{Mauri2018EssentialSO, title={Essential skeletons of pairs and the geometric P=W conjecture.}, author={Mirko Mauri and Enrica Mazzon and Matthew Stevenson}, journal={arXiv: Algebraic Geometry}, year={2018} }

We construct weight functions on the Berkovich analytification of a variety over a trivially-valued field of characteristic zero, and this leads to the definition of the Kontsevich-Soibelman skeletons and the essential skeletons of pairs. We prove that the weight functions determine a metric on the pluricanonical bundles which coincides with Temkin's canonical metric in the smooth case. The weight functions are defined in terms of log discrepancies, which makes the Kontsevich-Soibelman and… Expand

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