000			02376nam 2200313| 4500
001			85250
005			20220204102713.0
010			_a978-3-319-65907-7 _dcompra
090			_a85250
100			_a20190128d2017 k||y0pory50 ba
101			_aeng
102			_aCH
200			_aGeometric invariant theory _eover the real and complex numbers _bDocumento eletrónico _fNolan R. Wallach
210			_aCham _cSpringer _d2017
215			_aXIV, 190 p.
225			_aUniversitext
300			_aColocação: Online
303			_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.
410			_x0172-5939
606			_aGeometria algébrica
606			_aTeoria dos grupos
680			_aQA564
700			_aWallach _bNolan R.
801			_gRPC _aPT
856			_uhttps://doi.org/10.1007/978-3-319-65907-7
942			_2lcc _cF _n0