Geometry of the Plane Cremona Maps

Maria Alberich-Carramiñana (auth.)354042816X, 9783540428169

This book provides a self-contained exposition of the theory of plane Cremona maps, reviewing the classical theory. The book updates, correctly proves and generalises a number of classical results by allowing any configuration of singularities for the base points of the plane Cremona maps. It also presents some material which has only appeared in research papers and includes new, previously unpublished results. This book will be useful as a reference text for any researcher who is interested in the topic of plane birational maps.

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Table of contents :
1. Preliminaries….Pages 1-28
2. Plane Cremona maps….Pages 29-71
3. Clebsch’s theorems and jacobian….Pages 73-100
4. Composition….Pages 101-125
5. Characteristic matrices….Pages 127-176
6. Total principal and special homaloidal curves….Pages 177-205
7. Inverse Cremona map….Pages 207-225
8. Noether’s factorization theorem….Pages 227-247
References….Pages 249-251
Subject and Index Notation….Pages 253-256