Algebraic methods for vector bundles on non-Kähler elliptic fibrations

被引:0
作者
Brînzănescu V. [1 ]
机构
[1] Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest
关键词
Complex compact manifolds; Elliptic fibrations; Holomorphic vector bundles; Moduli spaces; Non-Kähler manifolds;
D O I
10.1007/s11565-017-0279-x
中图分类号
学科分类号
摘要
We survey some parts of the vast literature on holomorphic vector bundles on compact complex manifolds, focusing on the rank-two case vector bundles on non-Kähler elliptic fibrations. It is by no means intended to be a complete overview of this wide topic, but we rather focus on results obtained by the author and his collaborators. © 2017, Università degli Studi di Ferrara.
引用
收藏
页码:33 / 50
页数:17
相关论文
共 68 条
  • [1] Aprodu M., Brinzanescu V., Toma M., Holomorphic vector bundles on primary Kodaira surfaces, Math. Z, 242, pp. 63-73, (2002)
  • [2] Aprodu M., Moraru R., Toma M., Two-dimensional moduli spaces of vector bundles over Kodaira surfaces, Adv. Math, 231, 3-4, pp. 1202-1215, (2012)
  • [3] Atiyah M.F., Vector bundles over an elliptic curve, Proc. Lond. Math. Soc. (3), 7, pp. 414-452, (1957)
  • [4] Banica C., Le Potier J., Sur l’existence des fibrés vectoriels holomorphes sur les surfaces non-algebriques, J. Reine Angew. Math, 378, pp. 1-31, (1987)
  • [5] Barlet D., Espace analytique reduit des cycles analytiques complexes compact d’un espace analytique complexe de dimension finie, Seminaire Norguet 1974–1975, Springer LNM, (1975)
  • [6] Bartocci C., Bruzzo U., Hernandez Ruiperez D., Fourier–Mukai and Nahm Transforms in Geometry and Mathematical Physics, Progress in Mathematics, 276, (2009)
  • [7] Bartocci C., Bruzzo U., Hernandez Ruiperez D., Porras J.M., Mirror symmetry on K3 surfaces via Fourier–Mukai transform, Comm. Math. Phys, 195, pp. 79-93, (1998)
  • [8] Becker K., Becker M., Dasgupta K., Green P.S., Compactifications of heterotic theory on non-Kähler complex manifolds: I, JHEP, 304, (2003)
  • [9] Ben-Bassat O., Twisted derived equivalences, Trans. Am. Math. Soc, 361, 10, pp. 5469-5504, (2009)
  • [10] Borel A., A Spectral Sequence for Complex Analytic Bundles. Appendix II to F. Hirzebruch. Topological Methods in Algebraic Geometry, (1966)