Geometry of the plane Cremona maps / Maria Alberich-Carramiñana

Auteur: Alberich-Carramiñana, Maria (1971-) - AuteurType de document: Livre numériqueCollection: Lecture notes in mathematics, (Online) ; 1769Langue: anglaisÉditeur: Berlin : Springer, 2002 ISBN: 354042816X ISSN: 1617-9692Note: A birational transformation from the complex projective plane into itself is called a Cremona transformation. This is a very classical topic and the structure of the group of all plane Cremona transformations has received a good deal of attention in the modern literature. The aim of this book is not to focus on it, but to focus on a fixed but arbitrary Cremona transformation T filling in several gaps in the classical literature in which often the proofs assumed that the base points of T were not infinitely near base points. This book starts with the classical results in updated versions and presents a nice and reasonably self-contained exposition of the base points of a Cremona transformation. Hence this book is a must for anybody interested in the subject. In later chapters this book contains a few new results and gives for the first time complete proofs of some classical assertions. (Zentralblatt Sujets MSC: 14E05 Algebraic geometry -- Birational geometry -- Rational and birational maps
14E07 Algebraic geometry -- Birational geometry -- Birational automorphisms, Cremona group and generalizations
14H50 Algebraic geometry -- Curves -- Plane and space curves
En-ligne: Springerlink | Zentralblatt | MathSciNet

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A birational transformation from the complex projective plane into itself is called a Cremona transformation. This is a very classical topic and the structure of the group of all plane Cremona transformations has received a good deal of attention in the modern literature. The aim of this book is not to focus on it, but to focus on a fixed but arbitrary Cremona transformation T filling in several gaps in the classical literature in which often the proofs assumed that the base points of T were not infinitely near base points. This book starts with the classical results in updated versions and presents a nice and reasonably self-contained exposition of the base points of a Cremona transformation. Hence this book is a must for anybody interested in the subject. In later chapters this book contains a few new results and gives for the first time complete proofs of some classical assertions. (Zentralblatt

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