000			00403nam a2200145Ia 4500
999			_c170328 _d170328
020			_a3540569634
040			_cCUS
082			_a516.35 _bMUM/G
100			_aMumford, D.
245		0	_aGeometric invariant theory/ _cD. Mumford, J. Fogarty and F. Kirwan
250			_a3rd enl. ed.
260			_aBerlin: _bSpringer-Verlag, _cc1994.
300			_axiv, 292 p. : _bill. ; _c24 cm.
505			_aPreliminaries -- 1. Definitions -- 2. First properties -- 3. Good and bad actions -- 4. Further properties -- 5. Resume of some results of Grothendieck -- Fundamental theorems for the actions of reductive groups -- 1. Definitions -- 2. The affine case -- 3. Linearization of an invertible sheaf -- 4. The general case -- 5. Functional properties -- Analysis of stability -- 1. A numeral criterion -- 2. The flag complex -- 3. Applications -- An elementary example -- 1. Pre-stability -- 2. Stability -- 4. Further examples -- 1. Binary quantics -- 2. Hypersurfaces -- 3. Counter-examples -- 4. Sequences of linear subspaces -- 5. The projective adjoint action -- 6. Space curves -- The problem of moduli -- 1st construction -- 1. General discussion -- 2. Moduli as an orbit space -- 3. First chern classes -- 4. Utilization of 4.6 -- Abelian schemes -- 1. Duals -- 2. Polarizations -- 3. Deformations -- The method of covariants -- 2nd construction -- 1. The technique -- 2. Moduli as an orbit space -- 3. The covariant -- 4. Application to curves -- The moment map -- 1. Symplectic geometry -- 2. Symplectic quotients and geometric invariant theory -- 3. Kahler and hyperkahler quotients -- 4. Singular quotients -- 5. Geometry of the moment map -- 6. The cohomology of quotients: the symplectic case -- 7. The cohomology of quotients: the algebraic case -- 8. Vector bundles and the Yang-Mills functional -- 9. Yang-Mills theory over Riemann surfaces.
650			_aAlgebraic Geometry
650			_aInvariants
650			_aModuli theory
700			_aFogarty, J.
700			_aKirwan, F.
942			_cWB16