Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

Projective normality of the moduli space of rank $ 2$ vector bundles on a generic curve

Author(s): Takeshi Abe
Journal: Trans. Amer. Math. Soc. 362 (2010), 477-490.
MSC (2000): Primary 14H60, 14D20
Posted: August 12, 2009
MathSciNet review: 2550160
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We prove that the embedding to the projective space by the generalized theta divisors of the moduli space of rank $ 2$ vector bundles on a generic curve is projective normal.

References:

[A]
T. Abe: On $ SL(2)$-$ GL(n)$ strange duality, J. Math. Kyoto Univ., Vol. 46(3), 657-692, (2006). MR 2311364 (2008e:14012)

[B1]
A. Beauville: Fibrés de rang $ 2$ sur une courbe, fibré déterminant et fonctions thêta, Bull. Soc. Math. France 116 (1988), no. 4, 431-448. MR 1005388 (91b:14038)

[B2]
A. Beauville: Fibrés de rang deux sur une courbe, fibré déterminant et fonctions thêta II, Bull. Soc. Math. France 119 (1991), no. 3, 259-291. MR 1125667 (92m:14041)

[B3]
A. Beauville: Conformal blocks, fusion rules and the Verlinde formula, Proceedings of the Hirzebruch 65 Conference on Algebraic Geometry (Ramat Gan, 1993), 75-96, Israel Math. Conf. Proc., 9, Bar-Ilan Univ., Ramat Gan, 1996. MR 1360497 (97f:17025)

[B-L]
A. Beauville, Y. Laszlo: Conformal blocks and generalized theta functions, Comm. Math. Phys. 164 (1994), no. 2, 385-419. MR 1289330 (95k:14011)

[Bel]
P. Belkale: The Strange Duality Conjecture for Generic Curves, math. AG/0602018.

[Bho1]
U N. Bhosle: Tensor fields and singular principal bundles, Int. Math. Res. Not. 2004, no. 57, 3057-3077. MR 2098029 (2006f:14048)

[Bho2]
U N. Bhosle: Vector bundles with a fixed determinant on an irreducible nodal curve, Proc. Indian Acad. Sci. Math. Sci. 115 (2005), no. 4, 445-451. MR 2184204 (2007e:14054)

[B-V]
S. Brivio, A. Verra: The theta divisor of $ {\rm SU}\sb C(2,2d)\sp s$ is very ample if $ C$ is not hyperelliptic, Duke Math. J. 82 (1996), no. 3, 503-552. MR 1387683 (97e:14017)

[D-N]
J. M. Drezet, M. S. Narasimhan: Groupe de Picard des variétés de modules de fibrés semi-stables sur les courbes algébriques, Invent. Math. 97 (1989), no. 1, 53-94. MR 999313 (90d:14008)

[F]
G. Faltings: Moduli-stacks for bundles on semistable curves, Math. Ann. 304, 489-515 (1996). MR 1375622 (97d:14016)

[L]
Y. Laszlo: A propos de l'espace des modules de fibrés de rang $ 2$ sur une courbe, Math. Ann. 299 (1994), no. 4, 597-608. MR 1286886 (95f:14021)

[M-O]
A. Marian, D.  Oprea: The level-rank duality for non-abelian theta functions, Invent. Math. 168 (2007), no. 2, 225-247. MR 2289865 (2007k:14070)

[N-Rd]
M. S. Narasimhan, T. R. Ramadas: Factorisation of generalised theta functions. I, Invent. Math. 114 (1993), no. 3, 565-623. MR 1244913 (94i:14017)

[N-R]
M. S. Narasimhan, S. Ramanan: Moduli of vector bundles on a compact Riemann surface, Ann. of Math. (2) 89 1969 14-51. MR 0242185 (39:3518)

[Rd]
T. R. Ramadas: Factorisation of generalised theta functions. II. The Verlinde formula, Topology 35 (1996), no. 3, 641-654. MR 1396770 (97j:14014)

[R]
M. Raynaud: Sections des fibrés vectoriels sur une courbe, Bull. Soc. Math. France 110 (1982), no. 1, 103-125. MR 662131 (84a:14009)

[vG-I]
B. van Geemen, E. Izadi: The tangent space to the moduli space of vector bundles on a curve and the singular locus of the theta divisor of the Jacobian, J. Algebraic Geom. 10 (2001), no. 1, 133-177. MR 1795553 (2002e:14058)

[vG-P]
B. van Geemen, E. Previato: Prym varieties and the Verlinde formula, Math. Ann. 294 (1992), no. 4, 741-754. MR 1190454 (93j:14037)

[Sch1]
A. H. W. Schmitt: Singular principal $ G$-bundles on nodal curves, J. Eur. Math. Soc. (JEMS) 7 (2005), no. 2, 215-251. MR 2127994 (2005k:14070)

[Sch2]
A. H. W. Schmitt: Moduli spaces for semistable honest singular principal bundles on a nodal curve which are compatible with degeneration. A remark on U. N. Bhosle's paper: ``Tensor fields and singular principal bundles'', Int. Math. Res. Not. 2005, no. 23, 1427-1437. MR 2152237 (2007e:14019)

[S1]
X. Sun: Degeneration of moduli spaces and generalized theta functions, J. Algebraic Geom. 9 (2000), no. 3, 459-527. MR 1752012 (2001h:14040)

[S2]
X. Sun: Factorization of generalized theta functions in the reducible case, Ark. Mat. 41 (2003), no. 1, 165-202. MR 1971947 (2004c:14065)

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14H60, 14D20

Retrieve articles in all Journals with MSC (2000): 14H60, 14D20

Additional Information:

Takeshi Abe
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa, Sakyo-ku, Kyoto, 606-8502, Japan
Address at time of publication: Graduate School of Science and Technology, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan
Email: abeken@kurims.kyoto-u.ac.jp, abeken@sci.kumamoto-u.ac.jp

DOI: 10.1090/S0002-9947-09-04816-8
PII: S 0002-9947(09)04816-8
Received by editor(s): November 2, 2007
Received by editor(s) in revised form: May 2, 2008
Posted: August 12, 2009
Additional Notes: The author was partially supported by the Japanese Ministry of Education and Science, Grant-in-Aid for Young Scientists (B)
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia