LEADER 03666nam 22005535 450 001 9910254301503321 005 20200629194846.0 010 $a3-319-65907-3 024 7 $a10.1007/978-3-319-65907-7 035 $a(CKB)4100000000586903 035 $a(DE-He213)978-3-319-65907-7 035 $a(MiAaPQ)EBC6311779 035 $a(MiAaPQ)EBC5576626 035 $a(Au-PeEL)EBL5576626 035 $a(OCoLC)1004224826 035 $a(PPN)204534143 035 $a(EXLCZ)994100000000586903 100 $a20170908d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric Invariant Theory $eOver the Real and Complex Numbers /$fby Nolan R. Wallach 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XIV, 190 p.) 225 1 $aUniversitext,$x0172-5939 311 $a3-319-65905-7 327 $aPreface -- Part I. Background Theory -- 1. Algebraic Geometry -- 2. Lie Groups and Algebraic Groups -- Part II. Geometric Invariant Theory -- 3.  The Affine Theory -- 4. Weight Theory in Geometric Invariant Theory -- 5. Classical and Geometric Invariant Theory for Products of Classical Groups -- References -- Index. 330 $aGeometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers. This sophisticated topic is elegantly presented with enough background theory included to make the text accessible to advanced graduate students in mathematics and physics with diverse backgrounds in algebraic and differential geometry.  Throughout the book, examples are emphasized. Exercises add to the reader?s understanding of the material; most are enhanced with hints. The exposition is divided into two parts. The first part, ?Background Theory?, is organized as a reference for the rest of the book. It contains two chapters developing material in complex and real algebraic geometry and algebraic groups that are difficult to find in the literature. Chapter 1 emphasizes the relationship between the Zariski topology and the canonical Hausdorff topology of an algebraic variety over the complex numbers. Chapter 2 develops the interaction between Lie groups and algebraic groups. Part 2, ?Geometric Invariant Theory? consists of three chapters (3?5). Chapter 3 centers on the Hilbert?Mumford theorem and contains a complete development of the Kempf?Ness theorem and Vindberg?s theory. Chapter 4 studies the orbit structure of a reductive algebraic group on a projective variety emphasizing Kostant?s theory. The final chapter studies the extension of classical invariant theory to products of classical groups emphasizing recent applications of the theory to physics. 410 0$aUniversitext,$x0172-5939 606 $aAlgebraic geometry 606 $aGroup theory 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 615 0$aAlgebraic geometry. 615 0$aGroup theory. 615 14$aAlgebraic Geometry. 615 24$aGroup Theory and Generalizations. 676 $a512.5 700 $aWallach$b Nolan R$4aut$4http://id.loc.gov/vocabulary/relators/aut$041086 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254301503321 996 $aGeometric Invariant Theory$91562344 997 $aUNINA