Geometry of the plane Cremona maps / Maria Alberich-Carramiñana

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