We study the vortex equations for line bundles on compact Hermitian manifolds. We obtain a description of the moduli space of solutions of these equations in terms of effective divisors, which generalizes the known result in the Kähler case [B1].

References

[Bo] Booss, B.: Topologie und Analysis. Eine Einführung in die Atiyah-Singer-Indexformel, Universitext, Springer-Verlag, 1977
Google Scholar
[B1] Bradlow, S.: Vortices in Holomorphic Line Bundles over Closed Kähler Manifolds, Comm. Math. Phys. 135 (1990), 1–17
10.1007/BF02097654
Web of Science® Google Scholar
[B2] Bradlow, S.: Special Metrics and Stability for Holomorphic Bundles with Global Sections, J. Diff. Geom. 33 (1991), 169–214
10.4310/jdg/1214446034
Web of Science® Google Scholar
[BG] Bradlow, S., and Garcia-Prada, O.: Non-Abelian Monopoles and Vortices, Geometry and Physics (Aarhus, 1995), 567–589, Lecture Notes in Pure and Appl. Math. 184, Dekker, New York, 1997
Google Scholar
[BW] Bryan, J., and Wentworth, R.: The Multi-Monopole Equations for Kähler Surfaces, Turkish J. of Math. 20 (1996), 119–128
Google Scholar
[G] Gauduchon, P.: La 1-Forme de Torsion d'une Variete Hermitienne Compacte, Math. Ann. 267 (1984), 495–518
10.1007/BF01455968
Web of Science® Google Scholar
[KL] Kosarew, S., and Lupascu, P.: Moduli of Simple Holomorphic Pairs and Effective Divisors, preprint (Prépublication de l'Institut Fourier, Laboratoire de Mathématiques, No. 485/1999)
Google Scholar
[KW] Kazdan, J., and Warner, F.: Curvature Functions for Compact 2-Manifolds, Ann. Math. 99 (1974), 14–47
10.2307/1971012
Web of Science® Google Scholar
[LO] Lübke, M., and Okonek, Ch.: Moduli Spaces of Simple Bundles and Hermitian-Einstein Connections, Math. Ann. 276 (1987), 663–674
10.1007/BF01456994
Web of Science® Google Scholar
[LT] Lübke, M., and Teleman, A.: The Kobayashi-Hitchin Correspondence, World Scientific Publishing Co., 1995
Google Scholar
[L] Lupascu, P.: Seiberg-Witten Equations and Complex Surfaces, Ph. D. Thesis, Zürich, 1998
Google Scholar
[M] Miyajima, K.: Kuranishi Family of Vector Bundles and Algebraic Description of the Moduli Space of Einstein-Hermitian Connections, Publ. R. I. M. S., Kyoto Univ., 25 (1989), 301–320
10.2977/prims/1195173613
Web of Science® Google Scholar
[N] Nietlispach, B.: Seiberg-Witten Monopole auf Kählerflächen, Diplomarbeit Zürich, 1999
Google Scholar
[OT1] Okonek, Ch., and Teleman, A.: The Coupled Seiberg{Witten Equations, Vortices, Moduli Spaces of Stable Pairs, Internat. Journ. Math. Vol. 6, 6 (1995), 893–910
10.1142/S0129167X95000390
Web of Science® Google Scholar
[OT2] Okonek, Ch., and Teleman, A.: 3–Dimensional Seiberg-Witten Theory and Non-Kählerian Geometry, Math. Ann. 312 (1998), 261–288
10.1007/s002080050222
Web of Science® Google Scholar
[OT3] Okonek, Ch., and Teleman, A.: Seiberg-Witten Invariants for 4-Manifolds with b₊ = 0, to appear in “Memorial Volume dedicated to M. Schneider”
Google Scholar
[SY] Schoen, R., Yau, S.-T.: Lectures on Differential Geometry, Conference Proceedings and Lecture Notes in Geometry and Topology, Vol. 1, International Press (1994)
Google Scholar
[T] Teleman, A.: Stable Vector Bundles over Non-Kählerian Surfaces, Ph. D. Thesis, Zürich, 1993
Google Scholar

Citing Literature

Volume230, Issue1

October 2001

Pages 99-115

The Abelian Vortex Equations on Hermitian Manifolds

Abstract

References

Citing Literature

References

Information

About Wiley Online Library

Help & Support

Opportunities

Connect with Wiley

The Abelian Vortex Equations on Hermitian Manifolds

Abstract

References

Citing Literature

References

Related

Information