Poncelet Porisms and Beyond
Subtitle: Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics
By: by Vladimir Dragović, Milena Radnović
Contributors: Radnović, Milena; SpringerLink (Online service)
Series: Frontiers in Mathematics
Publisher: Springer Basel AG
Published: 2011
Place of publication: Basel
Language: eng
Format: [electronic resource] :
Number of pages: 293
ISBN-13: 9783034800143; 9783034800150
Subjects: Mathematics; Algebraic Geometry
Description: 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.