Cremona Transformations: In Plane and Space

by Hilda P. Hudson, Miles Reid, Vasilii A Iskovskikh (Foreword)

Hilda Hudson's book, first published in 1927, is the classic work on Cremona transformations. Her complete and elegant treatment of Cremona transformations of the plane in Part I was a central influence on 20th century work in algebraic geometry, singularity theory and algebra, and continues to inspire new research. Part II of the book, on 3-fold birational geometry, is more in the nature of a pioneering foray; current advances in higher dimensional geometry (Mori theory) provide for the first time adequate tools to discuss general cases of 3-fold birational transformations. This timely reissue of Hudson's book links ancient and modern algebraic its bibliography and historical sketch make the book an indispensable guide to the extensive early literature, while the detailed treatment of particular cases and the many unsolved questions on 3-fold birational geometry it raises present worthy challenges to current and future generations of 3-folders.

480 pages, Paperback

Published July 15, 2012