Variation of geometric invariant theory quotients
Publications Mathématiques de l'IHÉS, Volume 87 (1998), pp. 5-51.
@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},
     pages = {5--51},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {87},
     year = {1998},
     mrnumber = {2000b:14060},
     zbl = {01560390},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1998__87__5_0/}
}
TY  - JOUR
AU  - Dolgachev, Igor V.
AU  - Hu, Yi
TI  - Variation of geometric invariant theory quotients
JO  - Publications Mathématiques de l'IHÉS
PY  - 1998
SP  - 5
EP  - 51
VL  - 87
PB  - Institut des Hautes Études Scientifiques
UR  - http://www.numdam.org/item/PMIHES_1998__87__5_0/
LA  - en
ID  - PMIHES_1998__87__5_0
ER  - 
%0 Journal Article
%A Dolgachev, Igor V.
%A Hu, Yi
%T Variation of geometric invariant theory quotients
%J Publications Mathématiques de l'IHÉS
%D 1998
%P 5-51
%V 87
%I Institut des Hautes Études Scientifiques
%U http://www.numdam.org/item/PMIHES_1998__87__5_0/
%G en
%F PMIHES_1998__87__5_0
Dolgachev, Igor V.; Hu, Yi. Variation of geometric invariant theory quotients. Publications Mathématiques de l'IHÉS, Volume 87 (1998), pp. 5-51. http://www.numdam.org/item/PMIHES_1998__87__5_0/

[At] M. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), 1-15. | MR | Zbl

[B-B] A. Bialynicki-Birula, Some theorems on actions of algebraic groups, Ann. of Math. 98 (1973), 480-497. | MR | Zbl

[B-BS] A. Bialynicki-Birula and A. Sommese, Quotients by C* and SL(2, C) actions, Trans. Amer. Math. Soc. 279 (1983), 773-800. | MR | Zbl

[Bo] N. Bourbaki, Commutative Algebra, Berlin, New York, Springer-Verlag, 1989. | MR

[Br] M. Brion, 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 | Zbl

[BP] M. Brion and C. Procesi, 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 | Zbl

[GM] M. Goresky and R. Macpherson, On the topology of algebraic torus actions, in "Algebraic Groups, Utrecht 1986", Lect. Notes in Math. 1271 (1986), 73-90. | MR | Zbl

[GS] V. Guillemin and S. Sternberg, Birational equivalence in the symplectic category, Invent. Math. 97 (1989), 485-522. | MR | Zbl

[He] W. Hesselink, Desingularization of varieties of null forms, Invent. Math. 55 (1979), 141-163. | MR | Zbl

[Hu1] Y. Hu, The geometry and topology of quotient varieties of torus actions, Duke Math. Journal 68 (1992), 151-183. | MR | Zbl

[Hu2] Y. Hu, (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 | Zbl

[Ke] G. Kempf, Instability in invariant theory, Ann. of Math. 108 (1978), 299-316. | MR | Zbl

[KN] G. Kempf and L. Ness, The length of vectors in representation spaces, in "Algebraic geometry, Copenhagen 1978", Lecture Notes in Math. 732 (1979), Springer-Verlag, 233-243. | MR | Zbl

[Ki1] F. Kirwan, Cohomology of quotients in symplectic and algebraic geometry, Princeton University Press, 1984. | MR | Zbl

[Ki2] F. Kirwan, Partial desingularization of quotients of nonsinguler varieties and their Betti numbers, Annals of Math. 122 (1985), 41-85. | MR | Zbl

[KKV] F. Knop, H. Kraft, T. Vust, The Picard group of a G-variety, in "Algebraic transformation groups and invariant theory", DMV Seminar, B. 13, Birkhäuser, 1989, 77-87. | MR | Zbl

[K1] S. Kleiman, Towards a numerical criterion of ampleness, Annals of Math. (2) 84 (1966), 293-344. | MR | Zbl

[KSZ] M. Kapranov, B. Sturmfels, A. Zelevinsky, Quotients of toric varieties, Math. Ann. 290 (1991), 643-655. | EuDML | MR | Zbl

[Li] D. Lieberman, 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 | Zbl

[MFK] D. Mumford, J. Fogarty, F. Kirwan, Geometric Invariant Theory, 3rd edition, Berlin, New York, Springer-Verlag, 1994. | MR | Zbl

[Ne1] L. Ness, Mumford's numerical function and stable projective hypersurfaces, in "Algebraic geometry, Copenhagen 1978", Lecture Notes in Math. 732 (1979), Springer-Verlag, 417-453. | MR | Zbl

[Ne2] L. Ness, A stratification of the null cone via the moment map, Amer. Jour. of Math. 106 (1984), 1281-1325. | MR | Zbl

[Re] M. Reid, What is a flip, preprint, Utah, 1992, 17 p.

[Res] N. Ressayre, Variation de quotients en théorie des invariants, Mémoire de DEA ENS-Lyon, septembre 1996.

[Sj] R. Sjamaar, Holomorphic slices, symplectic reduction and multiplicities of representations, Annals of Math. 141 (1995), 87-129. | MR | Zbl

[Th1] M. Thaddeus, Stable pairs, linear systems and the Verlinde formula, Invent. Math. 117 (1994), 317-353. | EuDML | MR | Zbl

[Th2] M. Thaddeus, Geometric invariant theory and flips, Journal of the American Math. Society (to appear). | Zbl