Geometry of the Plane Cremona Maps: 1769 - Brossura

Alberich-Carraminana, Maria

Brossura

ISBN 10: 354042816X ISBN 13: 9783540428169

Casa editrice: Springer Berlin Heidelberg, 2008

Riassunto

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 It also presents some material which has only appeared in research papers and includes new, previously unpublished results.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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Contenuti

1. Preliminaries 1.1 Blowing-ups 1.2 Weighted clusters 1.3 Birational maps of surfaces 2. Plane Cremona maps 2.1 Base points 2.2 Principal curves 2.3 Contractile curves 2.4 Characteristic matrix 2.5 Equations of condition 2.6 Noether's inequality 2.7 Further relations 2.8 Quadratic plane Cremona maps 2.9 Transforming curves 3. Clebsch's theorems and jacobian 3.1 A Clebsch's theorem 3.2 The entries of the characteristic matrix 3.3 On symmetry of chararcteristics 3.4 Further properties 3.5 Jacobian of the homaloidal net 4. Composition 4.1 Composition of two plane Cremona maps 4.2 Consequences 5. Characteristic matrices 5.1 Homaloidal nets 5.2 Homaloidal types 5.3 On proper homaloidal types 5.4 Characteristic matrices 5.5 Exceptional types 5.6 On proper exceptional types 5.7 Weyl groups 6. Total principal and special homaloidal curves 6.1 Virtual versus effective behaviour 6.2 Non-expansive corresponding base points 6.3 Generic versus effective behaviour 6.4 Irreducible homaloidal curves 6.5 Special homaloidal curves 7 Inverse Cremona map 7.1 Non-expected contractile curves 7.2 Proximity among base points of the inverse 7.3 Inverse map and total principle curves 7.4 Consequences 8. Noether's factorization theorem 8.1 Criterion for homaloidal nets 8.2 Complexity and major base points 8.3 Resolution into the Jonquières maps 8.4 Resolution into quadratic maps 8.5 Resolution into ordinary quadratic maps

Product Description

Book by AlberichCarraminana Maria

Dettagli dell'edizione

• Editore: Springer Berlin Heidelberg
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 354042816X
• ISBN 13: 9783540428169
• Rilegatura: Copertina flessibile
• Numero di pagine: 280
• Contatto del produttore: non disponibile
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