@article{PMIHES_1998__87__5_0,
author = {Dolgachev, Igor V. and Hu, Yi},
title = {Variation of geometric invariant theory quotients},
journal = {Publications Math\'ematiques de l'IH\'ES},
volume = {S88},
year = {1998},
pages = {5-51},
mrnumber = {2000b:14060},
zbl = {01560390},
language = {en},
url = {http://dml.mathdoc.fr/item/PMIHES_1998__87__5_0}
}
Dolgachev, Igor V.; Hu, Yi. Variation of geometric invariant theory quotients. Publications Mathématiques de l'IHÉS, Tome S88 (1998) pp. 5-51. http://gdmltest.u-ga.fr/item/PMIHES_1998__87__5_0/
[At] , Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), 1-15. | MR 83e:53037 | Zbl 0482.58013
[B-B] , Some theorems on actions of algebraic groups, Ann. of Math. 98 (1973), 480-497. | MR 51 #3186 | Zbl 0275.14007
[B-BS] and , Quotients by C* and SL(2, C) actions, Trans. Amer. Math. Soc. 279 (1983), 773-800. | MR 85i:32045 | Zbl 0566.32026
[Bo] , Commutative Algebra, Berlin, New York, Springer-Verlag, 1989. | MR 90a:13001
[Br] , Sur l'image de l'application moment, in "Séminaire d'algèbre Paul Dubreil et Marie-Paule Malliavin", Lecture Notes in Math. 1296, Paris, 1986, 177-193. | MR 89i:32062 | Zbl 0667.58012
[BP] and , Action d'un tore dans une variété projective, in "Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory", Progress in Mathematics 192 (1990), Birkhäuser, 509-539. | MR 92m:14061 | Zbl 0741.14028
[GM] and , On the topology of algebraic torus actions, in "Algebraic Groups, Utrecht 1986", Lect. Notes in Math. 1271 (1986), 73-90. | MR 89a:14064 | Zbl 0633.14025
[GS] and , Birational equivalence in the symplectic category, Invent. Math. 97 (1989), 485-522. | MR 90f:58060 | Zbl 0683.53033
[He] , Desingularization of varieties of null forms, Invent. Math. 55 (1979), 141-163. | MR 81b:14025 | Zbl 0401.14006
[Hu1] , The geometry and topology of quotient varieties of torus actions, Duke Math. Journal 68 (1992), 151-183. | MR 93k:14019a | Zbl 0812.14031
[Hu2] , (W, R) matroids and thin Schubert-type cells attached to algebraic torus actions, Proc. of Amer. Math. Soc. 123 No. 9 (1995), 2607-2617. | MR 95k:14068 | Zbl 0867.14020
[Ke] , Instability in invariant theory, Ann. of Math. 108 (1978), 299-316. | MR 80c:20057 | Zbl 0406.14031
[KN] and , The length of vectors in representation spaces, in "Algebraic geometry, Copenhagen 1978", Lecture Notes in Math. 732 (1979), Springer-Verlag, 233-243. | MR 81i:14032 | Zbl 0407.22012
[Ki1] , Cohomology of quotients in symplectic and algebraic geometry, Princeton University Press, 1984. | MR 86i:58050 | Zbl 0553.14020
[Ki2] , Partial desingularization of quotients of nonsinguler varieties and their Betti numbers, Annals of Math. 122 (1985), 41-85. | MR 87a:14010 | Zbl 0592.14011
[KKV] , , , The Picard group of a G-variety, in "Algebraic transformation groups and invariant theory", DMV Seminar, B. 13, Birkhäuser, 1989, 77-87. | MR 1044586 | Zbl 0705.14005
[K1] , Towards a numerical criterion of ampleness, Annals of Math. (2) 84 (1966), 293-344. | MR 34 #5834 | Zbl 0146.17001
[KSZ] , , , Quotients of toric varieties, Math. Ann. 290 (1991), 643-655. | MR 92g:14050 | Zbl 0762.14023
[Li] , Compactness of the Chow scheme : applications to automorphisms and deformations of Kähler manifolds, in "Séminaire François Norguet 1975/77", Lect. Notes in Math. 670 (1978), 140-186. | MR 80h:32056 | Zbl 0391.32018
[MFK] , , , Geometric Invariant Theory, 3rd edition, Berlin, New York, Springer-Verlag, 1994. | MR 95m:14012 | Zbl 0797.14004
[Ne1] , Mumford's numerical function and stable projective hypersurfaces, in "Algebraic geometry, Copenhagen 1978", Lecture Notes in Math. 732 (1979), Springer-Verlag, 417-453. | MR 81e:14008 | Zbl 0442.14019
[Ne2] , A stratification of the null cone via the moment map, Amer. Jour. of Math. 106 (1984), 1281-1325. | MR 86c:14010 | Zbl 0604.14006
[Re] , What is a flip, preprint, Utah, 1992, 17 p.
[Res] , Variation de quotients en théorie des invariants, Mémoire de DEA ENS-Lyon, septembre 1996.
[Sj] , Holomorphic slices, symplectic reduction and multiplicities of representations, Annals of Math. 141 (1995), 87-129. | MR 96a:58098 | Zbl 0827.32030
[Th1] , Stable pairs, linear systems and the Verlinde formula, Invent. Math. 117 (1994), 317-353. | MR 95e:14006 | Zbl 0882.14003
[Th2] , Geometric invariant theory and flips, Journal of the American Math. Society (to appear). | Zbl 0874.14042