No Access

AUTOMORPHISMS OF MODULI SPACES OF SYMPLECTIC BUNDLES

School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India

Instituto de Ciencias Matemáticas, (CSIC-UAM-UC3M-UCM), C/Nicolás Cabrera 13-15, Campus Cantoblanco, 28049 Madrid, Spain

Search for more papers by this author

, and

VICENTE MUÑOZ

Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza Ciencias 3, 28040 Madrid, Spain

Search for more papers by this author

https://doi.org/10.1142/S0129167X12500528Cited by:11 (Source: Crossref)

Abstract

Let X be an irreducible smooth complex projective curve of genus g ≥ 4. Fix a line bundle L on X. Let M_Sp(L) be the moduli space of semistable symplectic bundles (E, φ : E ⊗ E → L) on X, with the symplectic form taking values in L. We show that the automorphism group of M_Sp(L) is generated by the automorphisms of the form E ↦ E ⊗ M, where , together with the automorphisms induced by automorphisms of X.

Keywords:

AMSC: 14H60

References

A. Beauville, M. S. Narasimhan and S. Ramanan, J. Reine Angew. Math. 398, 169 (1989). Web of Science, Google Scholar
U. N. Bhosle, Proc. Indian Acad. Sci. Math. Sci. 106, 403 (1996). Crossref, Web of Science, Google Scholar
I. Biswas and T. L. Gómez, Internat. J. Math. 17, 45 (2006). Link, Web of Science, Google Scholar
I. Biswas, T. L. Gómez and V. Muñoz, Automorphisms of moduli spaces of vector bundles over a curve, preprint . Google Scholar
I. Biswas and N. Hoffmann, A Torelli theorem for moduli spaces of principal bundles over a curve, to appear in Ann. Inst. Fourier . Google Scholar
J. Draisma, H. Kraft and J. Kuttler, Compos. Math. 142, 464 (2006). Crossref, Web of Science, Google Scholar
G. Faltings, J. Algebraic Geom. 2, 507 (1993). Google Scholar
N. J. Hitchin, Duke Math. J. 54, 91 (1987). Crossref, Web of Science, Google Scholar
J.-M. Hwang and S. Ramanan, Ann. Sci. École Norm. Sup. 37, 801 (2004). Crossref, Web of Science, Google Scholar
A. Kouvidakis and T. Pantev, Math. Ann. 302, 225 (1995). Crossref, Web of Science, Google Scholar
G. Laumon, Duke Math. J. 57, 647 (1988). Crossref, Web of Science, Google Scholar
C. T. Simpson, Publ. Math. Inst. Hautes Etudes Sci. 80, 5 (1995). Crossref, Google Scholar