Quotient spaces modulo algebraic groups

Annals of Mathematics

Volumn 145, Issue 1, 1997, Pages 33-79

  Kollár, János ^a  

^a UNIVERSITY OF UTAH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031503342     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/2951823     Document Type: Article

References (54)

1. M. ANDRé, Cinq exposés sur la désingularization (preprint).
2. A. ANDREOTTI and E. BOMBIERI, Sugli omeomorfismi delle varietá algebriche, Ann. Sci. Norm. Sup. Pisa 23 (1969), 430-450.
3. A. ANDREOTTI and F. NOGUET, La convexité holomorphe dans l'espace analytique des cycles d'une variété algébrique, Ann. Sci. Norm. Sup. Pisa 21 (1967), 31-82.
4. M. ATIYAH and I. MACDONALD, Introduction to Commutative Algebra, Addison-Wesley, 1969.
5. M. ARTIN, Algebraisation of formal moduli I., in Global Analysis, D. C. Spenser and S. Iyanaga eds., Univ. Tokyo Press - Princeton Univ. Press, 1969, pp. 21-71.
6. _, Algebraization of formal moduli II: Existence of modifications, Ann. of Math. 91 (1970), 83-135.
7. _, Versal deformations and algebraic stacks, Inv. Math. 27 (1974), 165-189.
8. S. BOSCH. W. LÜTKEBOHMERT, and M. RAYNAUD, Néron Models, Springer, 1990.
9. P. DELIGNE and D. MUMFORD, The irreducibility of space of curves of given genus, Publ. Math. IHES 36 (1969), 75-110.
10. M. DEMAZURE, Schémas en groupes réductifs, Bull. Soc. Math. France 93 (1967), 365-413.
11. G. DETHLOFF and H. GRAUERT, Seminormal complex spaces, in Several Complex Variables, Enc. of Math. Sci. vol. VII, Springer, 1994. pp. 183-220.
12. J. DIXMIER and M. RAYNAUD, Sur le quotient d'une variété algébrique, in Mathematical Analysis and Applications, L. Nachbin ed., Acad. Press, 1981, pp. 327-344.
13. A. GROTHENDIECK and J. DIEUDONNÉ, Eléments de Géométrie Algébrique, vol. 4, 8, 11, 17, 20, 24, 28, 32, Publ. Math. IHES, 1960-67.
14. _, Eléments de Géométrie Algébrique I., Springer, 1971.
15. J. FOGARTY, Geometric quotients are algebraic schemes, Adv. in Math. 48 (1983), 166-171.
16. G.-M. GREUEL and G. PFISTER, Geometric quotients of unipotent group actions, Proc. London Math. Soc. 67 (1993), 75-105.
17. H. HOLMANN, Quotientenräume komplexer Mannigfaltigkeiten, Math. Ann. 139 (1960), 383-402.
18. _, Quotienten komplexer Räume, Math. Ann. 142 (1961), 407-440.
19. _, Komplexe Räume mit komplexen Transformationsgruppen, Math. Ann. 150 (1963), 327-360.
20. B. KAUF, Äquivalenzrelationen auf allgemeinen komplexen Räumen, Schriftenreihe Math. Inst. Univ. Münster 39 (1968).
21. S. KEEL. Lecture at the 1994 Salt Lake City Summer School on Moduli.
22. S. KEEL and S. MORI, Quotients by groupoids (to appear).
23. D. KNUTSON, Algebraic Spaces, Springer Lecture Notes vol. 203, 1971.
24. J. KOLLÁR, Toward moduli of singular varieties, Comp. Math. 56 (1985), 369-398.
25. _, Projectivity of complete moduli, J. Diff. Geom. 32 (1990), 235-268.
26. _, Algebraic groups acting on schemes (preprint).
27. _, Rational Curves on Algebraic Varieties, Springer Verlag, Ergebnisse der Math. vol. 32, 1996.
28. D. LUNA. Slices étales, Bull. Soc. Math. France, Mémoires 33 (1973), 81-105.
29. H. MATSUMURA, Commutative Algebra, (second edition), Benjamin - Cummings, 1980.
30. T. MATSUSAKA, Polarised varieties with a given Hilbert polynomial, Amer. J. Math. 94 (1972), 1027-1077.
31. D. MUMFORD, Geometric Invariant Theory, Springer, 1965.
32. _, Abelian Varieties, Tata Inst. Lecture Notes, Oxford University Press, 1968.
33. D. MUMFORD and J. FOGARTY, Geometric Invariant Theory, 2nd edition, Springer, 1982.
34. M. NAGATA, On the fourteenth problem of Hilbert, Amer. J. Math. 81 (1959), 766-772.
35. _, Some questions on rational actions of groups, in Algebraic Geometry, Bombay, Oxford Univ. Press., 1969, pp. 323-334.
36. A. NEEMAN, Analytic questions in geometric invariant theory, in Invariant Theory, Contemp. Math. vol. 88, 1989, pp. 11-24.
37. D. POPESCU, General Néron desingularization, Nagoya Math. J. 100 (1985), 97-126; . . . and approximation, Nagoya Math. J. 104 (1986), 85-115.
38. D. POPESCU, General Néron desingularization, Nagoya Math. J. 100 (1985), 97-126; . . . and approximation, Nagoya Math. J. 104 (1986), 85-115.
39. H. POPP, On moduli of algebraic varieties I., Inv. Math. 22 (1973), 1-40; II., Comp. Math. 28 (1974), 51-81; III., Comp. Math. 31 (1975), 237-258.
40. H. POPP, On moduli of algebraic varieties I., Inv. Math. 22 (1973), 1-40; II., Comp. Math. 28 (1974), 51-81; III., Comp. Math. 31 (1975), 237-258.
41. H. POPP, On moduli of algebraic varieties I., Inv. Math. 22 (1973), 1-40; II., Comp. Math. 28 (1974), 51-81; III., Comp. Math. 31 (1975), 237-258.
42. M. ROBERTS, A note on coherent G-sheaves, Math. Ann. 275 (1986), 573-582.
43. C. S. SESHADRI, Some results on the quotient space by an algebraic group of automorphisms, Math. Ann. 149 (1963), 286-301.
44. _, Quotient spaces modulo reductive algebraic groups, Ann. of Math. 95 (1972), 511-556.
45. _, Geometric reductivity over an arbitrary base, Adv. in Math. 26 (1977), 225-274.
46. _, Fibrés Vectoriels sur les Courbes Algébriques. Astérisque vol. 96, Soc. Math. France, 1982.
47. A. Grothendieck, Revêtements Etales et Groupes Fondamental, Springer Lecture Notes 224, 1971.
48. M. DEMAZURE and A. GROTHENDIECK, Schémas en Groupes, Springer Lecture Notes vols. 151, 152, 153, 1970.
49. A. GROTHENDIECK, Cohomologie l-adique et Fonctions L, Springer Lecture Notes vol. 589, 1977.
50. M. SPIVAKOVSKY, Smoothing of ring homomorphisms (preprint).
51. C. TRAVERSO, Seminormality and the Picard group, Ann. Sci. E.N.S. Pisa 24 (1970), 585-595.
52. E. VIEHWEG, Quasi-Protective Moduli of Polarized Manifolds, Springer, 1995.
53. A. VISTOLI, Intersection theory on algebraic stacks and on their moduli spaces, Inv. Math. 97 (1989), 613-670.
54. A. WEIL, Foundations of Algebraic Geometry, AMS, 1962.