Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T23:07:40.671Z Has data issue: false hasContentIssue false

Moduli spaces of stable vector bundles on Enriques surfaces

Published online by Cambridge University Press:  22 January 2016

Hoil Kim*
Affiliation:
Topology and Geometry Research Center, Kyungpook National University, Taegu, Korea, [email protected]
Rights & Permissions [Opens in a new window]

Abstract.

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that the image of the moduli space of stable bundles on an Enriques surface by the pull back map is a Lagrangian subvariety in the moduli space of stable bundles, which is a symplectic variety, on the covering K3 surface. We also describe singularities and some other features of it.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

References

[Ar] Artin, M., Some numerical criteria for contractability of curves on algebraic surfaces, A. J. Math., 84 (1962), 485496.CrossRefGoogle Scholar
[Ba] Barth, W., Moduli of vector bundles on the projective plane, Invent. Math., 42 (1977), 6391.Google Scholar
[Bh] Bhosle, U. N., Net of quadrics and vector bundles on a double plane, Math. Z., 192 (1986), ??-??.Google Scholar
[B,P,V] Barth, W., Peters, C. and Ven, A. Van de, Compact Complex Surfaces, Springer-Verlag, 1984.Google Scholar
[Br] Brosius, E., Rank 2 vector bundles on a ruled surface I, II, Math. Ann., 265 (1983), 155168, Math. Ann., 266 (1983), 199214.Google Scholar
[C,D] F, Cossec. and Dolgachev, I., Enriques Surfaces I, Birkheuser 1989.Google Scholar
[D,K] Donaldson, S. K. and Kronheimer, P. B., The Geometry of Four Manifolds, Oxford, 1990.CrossRefGoogle Scholar
[D,R] Dolgachev, I. and Reider, I., On rank 2 vector bundles with and C2 = 3 on Enriques surfaces, LNM, Springer-Verlag, 1479 (1991).Google Scholar
[F] Friedman, R., Rank two vector bundles over regular elliptic surfaces, Invent Math., 96 (1989), 283332.Google Scholar
[Ha] Hartshorne, R., Algebraic Geometry, Springer-Verlag, 1977.Google Scholar
[Hu] Hulek, K., Stable rank 2 vector bundles on P2 with c1 odd, Math. Ann., 242 (1979), 241266.CrossRefGoogle Scholar
[Ki] Kim, H., Exceptional bundles on nodal Enriques surfaces, Manuscripta Math., 82 (1994), 113.Google Scholar
[Mu1] Mukai, S., Symplectic structure of the moduli space of sheaves on an abelian or K3 surface, Invent. Math., 77 (1984), 101116.Google Scholar
[Mu2] Mukai, S., On the moduli space of bundles on K3 surfaces I, Vector Bundles (Atiyah et al, ed.), Oxford Univ. Press, Bombay (1980), pp. 341413.Google Scholar
[O,S,S] Okonek, C., Schneider, M. and Spindler, H., Vector bundles on complex projective spaces, Progress in Math. Vol.3, Birkhauser, Boston (1980).Google Scholar
[O,V] Okonek, C. and Ven, A. Van de, Stable bundles and differential structures on certain elliptic surfaces, Invent Math., 86 (86), 357370.CrossRefGoogle Scholar
[Ta] Takemoto, F., Stable vector bundles on algebraic surfaces II, Nagoya Math. J., 52 (1973), 173195.CrossRefGoogle Scholar
[Ty1] Tyurin, A., Cycles, curves and vector bundles on an algebraic surface, Duke Math. J., 54 (1987), 126.Google Scholar
[Ty2] Tyurin, A., Symplectic structures on the varieties of moduli of vector bundles on algebraic surfaces with pg > 0, Math. USSR Izvestiya, 33, No.1 (1989), 139177.Google Scholar
[Q] Qin, Z., Moduli spaces of stable rank 2 bundles on ruled surfaces, Invent. Math., 110 (1992), 615626.Google Scholar