Projective Duality and Homogeneous Spaces

ISBN-13: 9783642061721 / Angielski / Miękka / 2010 / 250 str.

Evgueni A. Tevelev

Opis

Projective duality is a very classical notion naturally arising in various areas of mathematics, such as algebraic and differential geometry, combinatorics, topology, analytical mechanics, and invariant theory, and the results in this field were until now scattered across the literature. Thus the appearance of a book specifically devoted to projective duality is a long-awaited and welcome event. Projective Duality and Homogeneous Spaces covers a vast and diverse range of topics in the field of dual varieties, ranging from differential geometry to Mori theory and from topology to the theory of algebras. It gives a very readable and thorough account and the presentation of the material is clear and convincing. For the most part of the book the only prerequisites are basic algebra and algebraic geometry. This book will be of great interest to graduate and postgraduate students as well as professional mathematicians working in algebra, geometry and analysis.

Recenzje

"This book gives (mostly with proofs) everything related to projective duality in characteristic zero, from local stuff (second and higher fundamental forms) to the main classifications (Zak's theorems). Since homogeneous spaces arise in the classification of extremal varieties, it is natural to study in detail their properties with respect to duality. [...] It is written with enough details to be used for studying the topics."

Edoardo Ballico, Zentralblatt MATH 1071, 2005

"[...] In this survey the author gives a broad overview on the subject by showing that there are many different aspects of projective duality and it can be studied using a wide range of methods. The presentation of the material is clear and convincing and, by minimizing technical details, for most of the text the only prerequisites are basic algebraic geometry and theory of Lie groups. [...] The book will be of great interest to graduate and postgraduate students as well as professional mathematicians, presenting also a very large number of references on the subject."

Carla Dionisi, Mathematical Review Clippings 2005m

Spis treści

to Projective Duality.- Actions with Finitely Many Orbits.- Local Calculations.- Projective Constructions.- Vector Bundles Methods.- Degree of the Dual Variety.- Varieties with Positive Defect.- Dual Varieties of Homogeneous Spaces.- Self-dual Varieties.- Singularities of Dual Varieties.