Geometric invariant theory and flips

Journal of the American Mathematical Society

Volumn 9, Issue 3, 1996, Pages 691-723

  Thaddeus, Michael ^a,b  

^a ST JOHN S COLLEGE   (United Kingdom)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030531127     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0894-0347-96-00204-4     Document Type: Article

References (29)

1. M.F. Atiyah, On analytic surfaces with double points, Proc. R. Soc. Lond. A 247 (1958) 237-44. MR 20:2472
2. A. Bertram, G. Daskalopoulos, and R. Wentworth, Gromov invariants for holomorphic maps from Riemann surfaces to Grassmannians, J. Amer. Math. Soc., to appear.
3. U.N. Bhosle, Parabolic vector bundles on curves, Arkiv för Mat. 27 (1989) 15-22. MR 90f:14007
4. A. Bialynicki-Birula, Some theorems on actions of algebraic groups, Ann. Math. 98 (1973) 480-497. MR 51:3186
5. S. Bradlow, Special metrics and stability for holomorphic bundles with global sections, J. Diff. Geom. 33 (1991) 169-213. MR 91m:32031
6. S. Bradlow and G. Daskalopoulos, Moduli of stable pairs for holomorphic bundles over Riemann surfaces, Int. J. Math. 2 (1991) 477-513. MR 93b:58026
7. M. Brion and C. Procesi, Action d'un tore dans une variété projective, Operator algebras, unitary representations, enveloping algebras, and invariant theory, (A. Connes, M. Duflo, A. Joseph, and R. Rentschler, eds.), Birkhauser, 1990, pp. 509-539. MR 92m:14061
8. H. Boden and Y. Hu, Variation of moduli of parabolic bundles, Math. Ann., to appear.
9. I. Dolgachev and Y. Hu, Variation of geometric invariant theory quotients, preprint.
10. J.-M. Drezet and M.S. Narasimhan, Groupe de Picard des variétés de modules de fibrés semistables sur les courbes algébriques, Inv. Math. 97 (1989) 53-94. MR 90d:14008
11. J.J. Duistermaat and G.J. Heckman, On the variation in the cohomology of the symplectic form of the reduced phase space, Inv. Math. 69 (1982) 259-268. Addendum: 72 (1983) 153-158. MR 84h:58051a,b
12. D. Gieseker, On the moduli of vector bundles on an algebraic surface, Ann. of Math. 106 (1977) 45-60. MR 81h:14014
13. A. Grassi and J. Kollár, Log canonical models, Astérisque 211 (1992) 29-45. MR 94f:14013
14. A. Grothendieck, Sur quelques points d'algèbre homologique, Tôhoku Math. J. 9 (1957) 119-221. MR 21:1328
15. A. Grothendieck, Technique de descente et théorèmes d'existence en géométrie algébrique, IV: Les schémas de Hilbert, Sém. Bourbaki 1960-61, Exp. 221; reprinted in Fondements de la géométrie algébrique, Secrétariat Math., Paris, 1962. MR 26:3566
16. A. Grothendieck, Technique de descente et théorèmes d'existence en géométrie algébrique, IV: Les schémas de Hilbert, Sém. Bourbaki 1960-61, Exp. 221; reprinted in Fondements de la géométrie algébrique, Secrétariat Math., Paris, 1962. MR 26:3566
17. R. Hartshorne, Algebraic geometry, Springer-Verlag, 1977. MR 57:3116
18. Y. Hu, The geometry and topology of quotient varieties of torus actions, Duke Math. J. 68 (1992) 151-184. Erratum: 68 (1992) 609. MR 93k:14019a,b
19. F.C. Kirwan, Cohomology of quotients in algebraic and symplectic geometry, Princeton, 1984. MR 86i:58050
20. D. Luna, Slices étales, Mém. Soc. Math. France 33 (1973) 81-105. MR 49:7269
21. I.G. Macdonald, Symmetric products of an algebraic curve, Topology 1 (1962) 319-343. MR 27:1445
22. V.B. Mehta and C.S. Seshadri, Moduli of vector bundles on curves with parabolic structures, Math. Ann. 248 (1980) 205-239. MR 81i:14010
23. S. Mori, Flip theorem and the existence of minimal models for 3-folds, J. Amer. Math. Soc. 1 (1988) 117-253. MR 89a:14048
24. D. Mumford and J. Fogarty, Geometric invariant theory, second enlarged edition, Springer-Verlag, 1982. MR 86a:14006
25. P.E. Newstead, Introduction to moduli problems and orbit spaces, Tata Inst., Bombay, 1978. MR 81k:14002
26. C.S. Seshadri, Quotient spaces modulo reductive algebraic groups, Ann. of Math. 95 (1972) 511-556. MR 46:9044
27. C.S. Seshadri, Fibrés vectoriels sur les courbes algébriques, Astérisque 96 (1982). MR 85b:14023
28. M. Thaddeus, Stable pairs, linear systems and the Verlinde formula, Inv. Math. 117 (1994) 317-353. MR 95e:14006
29. M. Thaddeus, Toric quotients and flips, Proceedings of the 1993 Taniguchi symposium, (K. Fukaya, M. Furuta, and T. Kohno, eds.), World Scientific, 1994, pp. 193-213. MR 96b:14067