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Poncelet Porisms and Beyond

Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics

  • Vladimir Dragović
  • Milena Radnović

Part of the Frontiers in Mathematics book series (FM)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Vladimir Dragović, Milena Radnović
    Pages 1-9
  3. Vladimir Dragović, Milena Radnović
    Pages 11-25
  4. Vladimir Dragović, Milena Radnović
    Pages 27-66
  5. Vladimir Dragović, Milena Radnović
    Pages 67-105
  6. Vladimir Dragović, Milena Radnović
    Pages 107-135
  7. Vladimir Dragović, Milena Radnović
    Pages 137-164
  8. Vladimir Dragović, Milena Radnović
    Pages 165-202
  9. Vladimir Dragović, Milena Radnović
    Pages 203-225
  10. Vladimir Dragović, Milena Radnović
    Pages 227-257
  11. Vladimir Dragović, Milena Radnović
    Pages 259-277
  12. Back Matter
    Pages 279-293

About this book

Introduction

The goal of the book is to present, in a complete and comprehensive way, areas of current research interlacing around the Poncelet porism: dynamics of integrable billiards, algebraic geometry of hyperelliptic Jacobians, and classical projective geometry of pencils of quadrics. The most important results and ideas, classical as well as modern, connected to the Poncelet theorem are presented, together with a historical overview analyzing the classical ideas and their natural generalizations. Special attention is paid to the realization of the Griffiths and Harris programme about Poncelet-type problems and addition theorems. This programme, formulated three decades ago, is aimed to understanding the higher-dimensional analogues of Poncelet problems and the realization of the synthetic approach of higher genus addition theorems.

Keywords

algebraic geometry

Authors and affiliations

  • Vladimir Dragović
    • 1
  • Milena Radnović
    • 2
  1. 1., Mathematical InstituteSANUBelgradeSerbia
  2. 2., Mathematical InstituteSANUBelgradeSerbia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0015-0
  • Copyright Information Springer Basel AG 2011
  • Publisher Name Springer, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0014-3
  • Online ISBN 978-3-0348-0015-0
  • Series Print ISSN 1660-8046
  • Series Online ISSN 1660-8054
  • Buy this book on publisher's site