000			02689nam a22003377a 4500
003			OSt
005			20240625192137.0
008			240624b |||||||| |||| 00| 0 hin d
020			_a9783319659053
040			_aNISER LIBRARY _beng _cNISER LIBRARY
041			_aEnglish
082			_a512.7 _bWAL-G
100			_aWallach, Nolan R.
245			_aGeometric invariant theory : _bover the real and complex numbers
260			_aSwitzerland : _bSpringer, _c2017.
300			_axiv, 190p.
490			_aUniversitext, _x0172-5939
520			_aGeometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers. This sophisticated topic is elegantly presented with enough background theory included to make the text accessible to advanced graduate students in mathematics and physics with diverse backgrounds in algebraic and differential geometry. Throughout the book, examples are emphasized. Exercises add to the reader’s understanding of the material; most are enhanced with hints. The exposition is divided into two parts. The first part, ‘Background Theory’, is organized as a reference for the rest of the book. It contains two chapters developing material in complex and real algebraic geometry and algebraic groups that are difficult to find in the literature. Chapter 1 emphasizes the relationship between the Zariski topology and the canonical Hausdorff topology of an algebraic variety over the complex numbers. Chapter 2 develops the interaction between Lie groups and algebraic groups. Part 2, ‘Geometric Invariant Theory’ consists of three chapters (3–5). Chapter 3 centers on the Hilbert–Mumford theorem and contains a complete development of the Kempf–Ness theorem and Vindberg’s theory. Chapter 4 studies the orbit structure of a reductive algebraic group on a projective variety emphasizing Kostant’s theory. The final chapter studies the extension of classical invariant theory to products of classical groups emphasizing recent applications of the theory to physics.
650		0	_aAlgebraic geometry.
650		0	_aGroup theory.
650		0	_aHilbert-Mumford theorem
650		0	_aLie theory and invariant theory
650		0	_aGeometric invariant theory
650		0	_aCartan-Helgason theorem
650		0	_aLie groups
650		0	_aKostant cone
650		0	_aBorel fixed point theorem
856			_3Table of Contents _uhttps://link.springer.com/content/pdf/bfm:978-3-319-65907-7/1
856			_3Reviews _uhttps://www.goodreads.com/book/show/40177463-geometric-invariant-theory?from_search=true&from_srp=true&qid=NQrxQhJtW0&rank=1#CommunityReviews
942			_cN _2udc
999			_c35068 _d35068