|
A note on the Verlinde bundles on elliptic curves
Author(s):
Dragos
Oprea
Journal:
Trans. Amer. Math. Soc.
362
(2010),
3779-3798.
MSC (2000):
Primary 14H60;
Secondary 14H40
Posted:
February 17, 2010
MathSciNet review:
2601609
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We study the splitting properties of the Verlinde bundles over elliptic curves. Our methods rely on the explicit description of the moduli space of semistable vector bundles on elliptic curves, and on the analysis of the symmetric powers of the Schrödinger representation of the Theta group.
References:
-
- 1.
- M. Atiyah, Vector bundles over an elliptic curve, Proc. London Math. Soc., 7 (1957), 414-452. MR 0131423 (24:A1274)
- 2.
- A. Beauville, The Cobble hypersurfaces, C. R. Math. Acad. Sci. Paris, 337 (2003), no. 3, 189-194. MR 2001133 (2004k:14056)
- 3.
- P. Belkale, The strange duality conjecture for generic curves, J. Amer. Math. Soc. 21 (2008), 235-258. MR 2350055 (2009c:14059)
- 4.
- C. Birkenhake, H. Lange, Complex abelian varieties, Springer-Verlag, Berlin-New York, 1992. MR 1217487 (94j:14001)
- 5.
- F. Catanese, C. Ciliberto, Symmetric products of elliptic curves and surfaces of general type, J. of Alg. Geom. 2 (1993), 389-411. MR 1211993 (94i:14040)
- 6.
- 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)
- 7.
- R. Donagi, L. Tu, Theta functions for
 versus  , Math. Res. Lett. 1 (1994), no. 3, 345-357. MR 1302649 (95j:14012) - 8.
- J. Harris, W. Fulton, Representation Theory, Springer-Verlag, Berlin-New York, 1991. MR 1153249 (93a:20069)
- 9.
- G. Hein, D. Ploog, Stable bundles and Fourier-Mukai transforms on elliptic curves, Contributions to Algebra and Geometry 46 (2005), 423-434. MR 2196927 (2007a:14038)
- 10.
- 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)
- 11.
- S. Mukai, Duality between
 and  with its application to Picard sheaves, Nagoya Math. J. 81 (1981), 153-175. MR 607081 (82f:14036) - 12.
- D. Mumford, On equations defining abelian varieties I, Inventiones Math. 1 (1966), 287-354. MR 0204427 (34:4269)
- 13.
- D. Oprea, The Verlinde bundles and the semihomogeneous Wirtinger duality, submitted, arXiv:0831.4962.
- 14.
- A. Polishchuk, Abelian varieties, theta functions and the Fourier-Mukai transform, Cambridge University Press, Cambridge, 2003. MR 1987784 (2004m:14094)
- 15.
- M. Popa, Verlinde bundles and generalized theta linear series, Trans. Amer. Math. Soc., 354 (2002), no. 5, 1869-1898. MR 1881021 (2003i:14046)
- 16.
- L. Tu, Semistable bundles over an elliptic curve, Adv. Math 98 (1993), no. 1, 1-26. MR 1212625 (94a:14008)
- 17.
- J. Schulte, Harmonic analysis on finite Heisenberg groups, European J. Combin. 25 (2004), no. 3, 327-338. MR 2036470 (2005e:43009)
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (2000):
14H60,
14H40
Retrieve articles in all Journals with
MSC (2000):
14H60,
14H40
Additional Information:
Dragos
Oprea
Affiliation:
Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093
Email:
doprea@math.ucsd.edu
DOI:
10.1090/S0002-9947-10-05040-3
PII:
S 0002-9947(10)05040-3
Received by editor(s):
September 11, 2008
Posted:
February 17, 2010
Additional Notes:
This work was supported by NSF grant DMS-0701114
Copyright of article:
Copyright
2010,
American Mathematical Society
|
