Abstract
We describe the Chern classes of holomorphic vector bundles on non-algebraic complex torus of dimension 2.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Atiyah M.F. and Hirzebruch F. (1962). Analytic cycles on complex manifolds. Topology 1: 25–45
Bănică C. and Le Potier J. (1987). Sur l’existence des fibrés vectoriels holomorphes sur les surfaces non-algébriques. J. Reine Angew. Math. 378: 1–31
Brînzănescu, V.: Holomorphic vector bundles over compact complex surfaces. Lecture Notes in Mathematics, vol. 1624, pp. x+170. Springer, Berlin (1996)
Desale U.V. and Ramanan S. (1975). Poincaré polynomials of the variety of stable bundles. Math. Ann. 216: 233–244
Elencwajg G. and Forster O. (1982). Vector bundles on manifolds without divisors and a theorem on deformations. Ann. Inst. Fourier (Grenoble) 32(4): 25–51
Hirschowitz A. and Laszlo Y. (1995). À propos de l’existence de fibrés stables sur les surfaces. J. Reine Angew. Math. 460: 55–68
Harder G. and Narasimhan M.S. (1975). On the cohomology groups of moduli spaces of vector bundles on curves. Math. Ann. 212: 215–248
Huybrechts D. and Schröer S. (2003). The Brauer group of analytic K3 surfaces. Int. Math. Res. Not. 50: 2687–2698
Huybrechts, D., Stellari, P.: Equivalences of twisted K3 surfaces, math.AG/0409030
Mukai, S.: On the moduli space of bundles on K3 surfaces. I. In: Vector bundles on algebraic varieties (Bombay, 1984), pp. 341–413. Tata Inst. Fund. Res., Bombay (1987)
Schuster H.-W. (1982). Locally free resolutions of coherent sheaves on surfaces. J. Reine Angew. Math 337: 159–165
Schwarzenberger R.L.E. (1961). Vector bundles on algebraic surfaces. Proc. Lond. Math. Soc. 11(3): 601–622
Toma M. (1996). Stable bundles on non-algebraic surfaces giving rise to compact moduli spaces. C. R. Acad. Sci. Paris Sér. I Math. 323(5): 501–505
Toma M. (1999). Stable bundles with small c 2 over 2-dimensional complex tori. Math. Z. 232: 511–525
Teleman A. and Toma M. (2002). Holomorphic vector bundles on non-algebraic surfaces. C. R. Math. Acad. Sci. Paris 334(5): 383–388
Yoshioka K. (1994). The Betti numbers of the moduli space of stable sheaves of rank 2 on P 2. J. Reine Angew. Math. 453: 193–220
Yoshioka K. (1995). The Betti numbers of the moduli space of stable sheaves of rank 2 on a ruled surface. Math. Ann. 302: 519–540
Yoshioka K. (2001). Moduli spaces of stable sheaves on abelian surfaces. Math. Ann. 321: 817–884. math.AG/0009001
Yoshioka K. (2003). Twisted stability and Fourier–Mukai transform I. Compos. Math. 138: 261–288
Yoshioka K. (2006). Moduli of twisted sheaves on a projective variety. math.AG/0411538. Adv. Stud. Pure Math. 45: 1–30
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kurihara, K., Yoshioka, K. Holomorphic vector bundles on non-algebraic tori of dimension 2. manuscripta math. 126, 143–166 (2008). https://doi.org/10.1007/s00229-008-0169-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00229-008-0169-8