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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, hikim@bh.kyungpook.ac.kr
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Abstract.

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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