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Overview"This volume grew out of two Simons Symposia on ""Nonarchimedean and tropical geometry"" which took place on the island of St. John in April 2013 and in Puerto Rico in February 2015. Each meeting gathered a small group of experts working near the interface between tropical geometry and nonarchimedean analytic spaces for a series of inspiring and provocative lectures on cutting edge research, interspersed with lively discussions and collaborative work in small groups. The articles collected here, which include high-level surveys as well as original research, mirror the main themes of the two Symposia. Topics covered in this volume include: Differential forms and currents, and solutions of Monge-Ampere type differential equations on Berkovich spaces and their skeletons; The homotopy types of nonarchimedean analytifications; The existence of ""faithful tropicalizations"" which encode the topology and geometry of analytifications; Relations between nonarchimedean analytic spaces and algebraic geometry, including logarithmic schemes, birational geometry, and the geometry of algebraic curves; Extended notions of tropical varieties which relate to Huber's theory of adic spaces analogously to the way that usual tropical varieties relate to Berkovich spaces; and Relations between nonarchimedean geometry and combinatorics, including deep and fascinating connections between matroid theory, tropical geometry, and Hodge theory." Full Product DetailsAuthor: Matthew Baker , Sam PaynePublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: Softcover reprint of the original 1st ed. 2016 Dimensions: Width: 15.50cm , Height: 2.80cm , Length: 23.50cm Weight: 8.073kg ISBN: 9783319809243ISBN 10: 3319809245 Pages: 526 Publication Date: 09 June 2018 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsPreface.- Forms and currents on the analytification of an algebraic variety (after Chambert-Loir and Ducros) [W. Gubler].- Convergence Polygons for Connections on Nonarchimedean Curves [K.S. Kedlaya].- About Hrushovski and Loeser's work on the Homotopy Type of Berkovich Spaces [A. Ducros].- Excluded Homeomorphism Types for Dual Complexes of Surfaces [D. Cartwright].- Analytification and Tropicalization over Non-Archimedean Fields [A. Werner].- Berkovich Skeleta and Birational Geometry [J. Nicaise].- Metrization of Differential Pluriforms on Berkovich Analytic Spaces [M. Temkin].- Skeletons and Fans of Logarithmic Structures [D. Abramovich, Q. Chen, S. Marcus, M. Ulirsch, and J. Wise].- Introduction to Adic Tropicalization [T. Foster].- Degeneration of Linear Series from the Tropical Point of View and Applications [M. Baker and D. Jensen].- Matroid Theory for Algebraic Geometries [E. Katz].ReviewsAuthor InformationMatthew BakerDepartment of MathematicsGeorgia Institute of TechnologyAtlanta, Georgia mbaker@math.gatech.eduSam Payne Department of Mathematics Yale University New Haven, Connecticut sam.payne@yale.edu Tab Content 6Author Website:Countries AvailableAll regions |
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