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100   $a20091109j20080704  fy             0
101 0 $aeng
135   $aurnn|mmmmamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aGeometric Invariant Theory and Decorated Principal Bundles$b[electronic resource] /$fAlexander H.W. Schmitt
210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2008
215   $a1 online resource (396 pages)
225 0 $aZurich Lectures in Advanced Mathematics (ZLAM)
330   $aThe book starts with an introduction to Geometric Invariant Theory (GIT). The fundamental results of Hilbert and Mumford are exposed as well as more recent topics such as the instability flag, the finiteness  of the number of quotients, and the variation of quotients.  In the second part, GIT is applied to solve the classification problem of decorated principal bundles on a compact Riemann surface. The solution is a quasi-projective moduli scheme which parameterizes those objects that satisfy a semistability condition originating from gauge theory. The moduli space is equipped with a generalized Hitchin map.  Via the universal Kobayashi-Hitchin correspondence, these moduli spaces are related to moduli spaces of solutions of certain vortex type equations. Potential applications include the study of representation spaces of the fundamental group of compact Riemann surfaces.  The book concludes with a brief discussion of generalizations of these findings to higher dimensional base varieties, positive characteristic, and parabolic bundles.  The text is fairly self-contained (e.g., the necessary background from the theory of principal bundles is included) and features numerous examples and exercises. It addresses students and researchers with a working knowledge of elementary algebraic geometry.
606   $aAlgebraic geometry$2bicssc
606   $aFields & rings$2bicssc
606   $aAlgebraic geometry$2msc
606   $aCommutative rings and algebras$2msc
615 07$aAlgebraic geometry
615 07$aFields & rings
615 07$aAlgebraic geometry
615 07$aCommutative rings and algebras
686   $a14-xx$a13-xx$2msc
700   $aSchmitt$b Alexander H.W.$01070607
801  0$bch0018173
906   $aBOOK
912   $a9910151934603321
996   $aGeometric Invariant Theory and Decorated Principal Bundles$92564458
997   $aUNINA