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Theta functions on moduli spaces of  -bundles
Author(s):
Gerd
Faltings
Journal:
J. Algebraic Geom.
18
(2009),
309-369.
Posted:
May 28, 2008
MathSciNet review:
2475817
Retrieve article in:
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Abstract |
References |
Additional information
Abstract:
We extend results on the Hitchin fibration to positive characteristics. We derive from the Verlinde formula the existence of canonical divisors on moduli space of  -bundles, first in characteristic zero and then (using the previous) also in positive characteristics. It remains open to give a geometric definition. We compute the central charge for some geometrically defined divisors.
References:
-
- 1.
- N.Bourbaki, Groupes et algèbres de Lie, Hermann, Paris 1968. MR 0240238 (39:1590)
- 2.
- A.Beauville, M.S.Narasimhan, S.Ramanan, Spectral curves and the generalised theta divisor, J. Reine Angew. Math. 398 (1989), 169-179. MR 998478 (91c:14040)
- 3.
- R.Y.Donagi, D.Gaitsgory, The gerbe of Higgs bundles, Transformation groups 7 (2002), 109-153. MR 1903115 (2003e:14034)
- 4.
- G.Faltings, Stable C-bundles and projective connections, Journ. of Algebr. Geom. 2 (1993), 507-568. MR 1211997 (94i:14015)
- 5.
- G.Faltings, A proof for the Verlinde formula, Journ. of Algebr. Geom. 3 (1994), 347-374. MR 1257326 (95j:14013)
- 6.
- G.Faltings, Algebraic loop groups and moduli spaces of bundles, J. Eur. Math. Soc. 5 (2003), 41-68. MR 1961134 (2003k:14011)
- 7.
- N.J.Hitchin, Stable bundles and integrable connections, Duke Math. J. 54 (1987), 91-114. MR 885778 (88i:58068)
- 8.
- J.E.Humphreys, Linear algebraic groups.
- 9.
- F.F.Knudsen, D.Mumford, The projectivity of the space of stable curves I, Math. Scand. 39 (1976), 19-55 Springer-Verlag, New York 1975. MR 0437541 (55:10465)
- 10.
- R.W.Richardson, Conjugacy classes in Lie algebras and algebraic groups, Ann. of Math. 86(1967), 1-15. MR 0217079 (36:173)
- 11.
- C.Sorger, On moduli of G-bundles on a curve for exceptional G, Ann. Sci. Éc. Norm. Supér. 32 (1999), 127-133. MR 1670528 (99m:14031)
- 12.
- N.Spaltenstein, Existence of transversal slices to nilpotent orbits in good characteristics, J. Fac. Sci. Univ. of Tokyo 31(1984), 283-286. MR 763422 (86c:14035)
- 13.
- A.Tsuchiya, K.Ueno, Y.Yamada, Conformal field theories on universal families of stable curves with gauge symmetries, Adv. Stud. Pure Math. 19 (1989), 459-566. MR 1048605 (92a:81191)
Additional Information:
Gerd
Faltings
Affiliation:
Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
PII:
S 1056-3911(08)00499-2
Received by editor(s):
January 16, 2007
Received by editor(s) in revised form:
September 27, 2007
Posted:
May 28, 2008
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