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Nonarchimedean and Tropical Geometry de Matthew Baker

Nonarchimedean and Tropical Geometry: Simons Symposia

Editat de Matthew Baker, Sam Payne
en Limba Engleză Paperback – 9 iun 2018
Thisvolume grew out of two Simons Symposia on "Nonarchimedean and tropicalgeometry" which took place on the island of St. John in April 2013 and inPuerto Rico in February 2015. Each meeting gathered a small group of expertsworking near the interface between tropical geometry and nonarchimedeananalytic spaces for a series of inspiring and provocative lectures on cuttingedge research, interspersed with lively discussions and collaborative work insmall groups. The articles collected here, which include high-level surveys aswell as original research, mirror the main themes of the two Symposia.
Topicscovered in this volume include: 
  • Differential forms and currents, andsolutions of Monge-Ampere type differential equations on Berkovich spaces andtheir skeletons; 
  • The homotopy types of nonarchimedean analytifications;
  • The existence of "faithful tropicalizations" which encode the topology andgeometry of analytifications;
    • Relations between nonarchimedean analyticspaces and algebraic geometry, including logarithmic schemes, birationalgeometry, and the geometry of algebraic curves;
  • Extended notions oftropical varieties which relate to Huber's theory of adic spaces analogously tothe way that usual tropical varieties relate to Berkovich spaces; and 
  • Relationsbetween nonarchimedean geometry and combinatorics, including deep andfascinating connections between matroid theory, tropical geometry, and Hodgetheory.
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Specificații

ISBN-13: 9783319809243
ISBN-10: 3319809245
Ilustrații: XIV, 526 p. 89 illus., 10 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.75 kg
Ediția:Softcover reprint of the original 1st ed. 2016
Editura: Springer International Publishing
Colecția Springer
Seria Simons Symposia

Locul publicării:Cham, Switzerland

Cuprins

Preface.- 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]. 

Textul de pe ultima copertă

This volume grew outof two Simons Symposia on "Nonarchimedean and tropical geometry"which took place on the island of St. John in April 2013 and in Puerto Rico inFebruary 2015. Each meeting gathered a small group of experts working near theinterface between tropical geometry and nonarchimedean analytic spaces for aseries 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 asoriginal research, mirror the main themes of the two Symposia.
Topics covered inthis volume include: 
  • Differential forms and currents, and solutions of Monge–Ampère 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.

Caracteristici

Includes supplementary material: sn.pub/extras