Projective Duality and Homogeneous Spaces

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.

Results up until this preprint were scattered across the literature with several researchers in the area apparently unaware of each other's work Brings together all known (at least to this reviewer) results on the subject Includes supplementary material: sn.pub/extras

Inhalt
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.