Nonarchimedean and Tropical Geometry

Matthew Baker

ISBN 10: 3319809245 / ISBN 13: 9783319809243

Published by Springer, 2018

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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; andRelationsbetween nonarchimedean geometry and combinatorics, including deep andfascinating connections between matroid theory, tropical geometry, and Hodgetheory.

Seller Inventory # 9783319809243

Bibliographic Details

• Title: Nonarchimedean and Tropical Geometry
• Publisher: Springer
• Publication Date: 2018
• Language: English
• ISBN 10: 3319809245
• ISBN 13: 9783319809243
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 29D millimeters 235 millimeters width by 155 millimeters height by 29 millimeters depth
• Weight: 809 grams

About this title

Synopsis

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.
  

About the Author

Matthew BakerDepartment of MathematicsGeorgia Institute of TechnologyAtlanta, Georgia
mbaker@math.gatech.edu

Sam Payne
Department of Mathematics
Yale University
New Haven, Connecticut
sam.payne@yale.edu