Weight functions on non-Archimedean analytic spaces and the Kontsevich–Soibelman skeleton

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Title: Weight functions on non-Archimedean analytic spaces and the Kontsevich–Soibelman skeleton
Authors: Mustaţă, M
Nicaise, J
Item Type: Journal Article
Abstract: We associate a weight function to pairs consisting of a smooth and proper variety X over a complete discretely valued field and a differential form on X of maximal degree. This weight function is a real-valued function on the non-archimedean analytification of X. It is piecewise affine on the skeleton of any regular model with strict normal crossings of X, and strictly ascending as one moves away from the skeleton. We apply these properties to the study of the Kontsevich-Soibelman skeleton of such a pair, and we prove that this skeleton is connected when X has geometric genus one. This result can be viewed as an analog of the Shokurov-Kollar connectedness theorem in birational geometry.
Issue Date: 1-Jul-2015
Date of Acceptance: 28-Nov-2014
URI: http://hdl.handle.net/10044/1/30659
DOI: https://dx.doi.org/10.14231/AG-2015-016
Publisher: Foundation Compositio Mathematica
Start Page: 365
End Page: 404
Journal / Book Title: Algebraic Geometry
Volume: 2
Issue: 3
Copyright Statement: This journal is © Foundation Compositio Mathematica 2015. This article is distributed with Open Access under the terms of the Creative Commons Attribution Non-Commercial License, which permits non-commercial reuse, distribution, and reproduction in any medium, provided that the original work is properly cited. For commercial re-use, please contact the Foundation Compositio Mathematica.
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: 306610
Keywords: math.AG
14G22 (Primary) 13A18, 14F17 (Secondary)
Publication Status: Published
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences

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