# Structure of Algebraic Groups and Geometric Applications

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*Michael Brion; Preena Samuel; V. Uma*

A publication of Hindustan Book Agency

This book originates from a series of 10 lectures given by
Michel Brion at the Chennai Mathematical Institute during January 2011. The
book presents Chevalley's theorem 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, 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.

A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

#### Readership

Graduate students and research mathematicians interested in algebraic geometry.