Principal bundles over a projective scheme

Hyeon, Donghoon

doi:10.1090/S0002-9947-01-02933-6

Principal bundles over a projective scheme
HTML articles powered by AMS MathViewer

by Donghoon Hyeon PDF

Trans. Amer. Math. Soc. 354 (2002), 1899-1908 Request permission

Abstract:

We prove the existence of a quasi-projective moduli scheme for principal bundles over an arbitrary projective scheme.

References

Paul S. Aspinwall and Ron Y. Donagi, The heterotic string, the tangent bundle and derived categories, Adv. Theor. Math. Phys. 2 (1998), no. 5, 1041–1074. MR 1688481, DOI 10.4310/ATMP.1998.v2.n5.a4
B. Balaji and C.S, Seshadri, Semistable principal bundles, Preprint (1999).
Ron Donagi, Taniguchi lectures on principal bundles on elliptic fibrations, Integrable systems and algebraic geometry (Kobe/Kyoto, 1997) World Sci. Publ., River Edge, NJ, 1998, pp. 33–46. MR 1672104
Ron Y. Donagi, Principal bundles on elliptic fibrations, Asian J. Math. 1 (1997), no. 2, 214–223. MR 1491982, DOI 10.4310/AJM.1997.v1.n2.a1
R. Friedman and J. W. Morgan, Holomorphic principal bundles over elliptic curves, Preprint (1998), math.AG/9811130.
R. Friedman and J. W. Morgan, Holomorphic principal bundles over elliptic curves II : The parabolic construction, Preprint (2000), math.AG/0006174.
Robert Friedman, John W. Morgan, and Edward Witten, Principal $G$-bundles over elliptic curves, Math. Res. Lett. 5 (1998), no. 1-2, 97–118. MR 1618343, DOI 10.4310/MRL.1998.v5.n1.a8
D. Gieseker, On the moduli of vector bundles on an algebraic surface, Ann. of Math. (2) 106 (1977), no. 1, 45–60. MR 466475, DOI 10.2307/1971157
Séminaire Bourbaki, 13ième année: 1960/61. Textes des conférences. Exposés 205 à 222, Secrétariat mathématique, Paris, 1961 (French). Deuxième édition, corrigée. 3 fascicules. MR 0151353
Peter Scherk, Bemerkungen zu einer Note von Besicovitch, J. London Math. Soc. 14 (1939), 185–192 (German). MR 29, DOI 10.1112/jlms/s1-14.3.185
Daniel Huybrechts and Manfred Lehn, The geometry of moduli spaces of sheaves, Aspects of Mathematics, E31, Friedr. Vieweg & Sohn, Braunschweig, 1997. MR 1450870, DOI 10.1007/978-3-663-11624-0
D. Mumford, J. Fogarty, and F. Kirwan, Geometric invariant theory, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results in Mathematics and Related Areas (2)], vol. 34, Springer-Verlag, Berlin, 1994. MR 1304906, DOI 10.1007/978-3-642-57916-5
Nelson Dunford, A mean ergodic theorem, Duke Math. J. 5 (1939), 635–646. MR 98
A. Ramanathan and S. Subramanian, Einstein-Hermitian connections on principal bundles and stability, J. Reine Angew. Math. 390 (1988), 21–31. MR 953674
C. S. Seshadri, Quotient spaces modulo reductive algebraic groups, Ann. of Math. (2) 95 (1972), 511–556; errata, ibid. (2) 96 (1972), 599. MR 309940, DOI 10.2307/1970870
Hermann Kober, Transformationen von algebraischem Typ, Ann. of Math. (2) 40 (1939), 549–559 (German). MR 96, DOI 10.2307/1968939