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Published: July 2009

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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 Jonquiéres maps 8.4 Resolution into quadratic maps 8.5 Resolution into ordinary quadratic maps

ISBN: 9783540428169
ISBN-10: 354042816X
Series: Springer Series in Synergetics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 280
Published: July 2009
Publisher: SPRINGER VERLAG GMBH
Dimensions (cm): 23.393 x 15.596  x 1.499
Weight (kg): 0.395