Frontiers in Mathematics: Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics

Dragović, Vladimir; Radnović, Milena

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.

Details

Published by: Birkhäuser

Publication Date: 2011-05-06

Format: Paperback

ISBN-13: 9783034800143

DOI: 10.1007/978-3-0348-0015-0

Dimensions: 240cm x168cm

Pages: 294