Fr. 331.00

Nonarchimedean and Tropical Geometry

English · Hardback

Shipping usually within 3 to 5 weeks (title will be specially ordered)

Description

Read more

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.

List of contents

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]. 

About the author










Matthew BakerDepartment of MathematicsGeorgia Institute of TechnologyAtlanta, Georgia
mbaker@math.gatech.eduSam Payne
Department of Mathematics
Yale University
New Haven, Connecticut
sam.payne@yale.edu

Summary

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.

Product details

Assisted by Matt Baker (Editor), Matthe Baker (Editor), Matthew Baker (Editor), Payne (Editor), Payne (Editor), Sam Payne (Editor)
Publisher Springer, Berlin
 
Languages English
Product format Hardback
Released 01.01.2016
 
EAN 9783319309446
ISBN 978-3-31-930944-6
No. of pages 526
Dimensions 162 mm x 239 mm x 36 mm
Weight 972 g
Illustrations XIV, 526 p. 89 illus., 10 illus. in color.
Series Simons Symposia
Simons Symposia
Subject Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra

Customer reviews

No reviews have been written for this item yet. Write the first review and be helpful to other users when they decide on a purchase.

Write a review

Thumbs up or thumbs down? Write your own review.

For messages to CeDe.ch please use the contact form.

The input fields marked * are obligatory

By submitting this form you agree to our data privacy statement.