
Lectures on the Structure of Algebraic Groups and Geometric Applications
Hindustan Book Agency (Publisher)
Published on 30. January 2013
Book
Paperback/Softback
128 pages
978-93-80250-46-5 (ISBN)
Description
This book originates from a series of 10 lectures given by Professor Michel Brion at the Chennai Mathematical Institute during January 2011. The book presents a theorem due to Chevalley on the structure of connected algebraic groups, over algebraically closed fields, as the starting point of various other structure results developed in the recent past. Chevalley's structure theorem states that any connected algebraic group over an algebraically closed field is an extension of an abelian variety by a connected affine algebraic group. This theorem forms the foundation for the classification of anti-affine groups which plays a central role in the development of the structure theory of homogeneous bundles over abelian varieties and for the classification of complete homogeneous varieties. All these results are presented in this book. The book begins with an overview of the results exposed, the proofs of which constitute the rest of the book. Various open questions also have been indicated in the course of the exposition.
This book assumes certain preliminary knowledge of linear algebraic groups, abelian varieties and algebraic geometry. The book is intended for graduate students and researchers in algebraic geometry.
This book assumes certain preliminary knowledge of linear algebraic groups, abelian varieties and algebraic geometry. The book is intended for graduate students and researchers in algebraic geometry.
More details
Language
English
Place of publication
New Delhi
India
Target group
Professional and scholarly
Dimensions
Height: 235 mm
Width: 155 mm
Weight
230 gr
ISBN-13
978-93-80250-46-5 (9789380250465)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Michel Brion | Preena Samuel
Lectures on the structure of algebraic groups and geometric applications
E-Book
01/2013
1st Edition
Hindustan Book Agency
€32.09
Available for download
Persons
Michel Brion, Institut Fourier, Grenoble, France.
Preena Samue, Chennai Mathematical Institute, Chennai, India.
V. Uma, Indian Institute of Technology Madras, Chennai, India.
Preena Samue, Chennai Mathematical Institute, Chennai, India.
V. Uma, Indian Institute of Technology Madras, Chennai, India.
Content
1 Overview 2 Proof of Chevalley's Theorem 3 Applications and developments 4 Complete homogeneous varieties 5 Anti-affine groups 6 Homogeneous vector bundles 7 Homogeneous principal bundles Bibliography Index