Holomorphic vector bundles on non-algebraic surfaces

Teleman, Andrei; Toma, Matei

HAL, hal-00881747 / Harvested from HAL

Résumé

The existence problem for holomorphic structures on vector bundles over non-algebraic surfaces is in general still open. We solve this problem in the case of rank 2 vector bundles over K3 surfaces and in the case of vector bundles of arbitrary rank over all known surfaces of class VII. Our methods, which are based on Donaldson theory and deformation theory, can be used to solve the existence problem of holomorphic vector bundles on further classes of non-algebraic surfaces.

Publié le : 2002-07-05
Classification: Complex surface, Holomorphic bundle, Vector bundle, Non algebraic surface, Donaldson invariants, MSC 32L05, 32L10, 32Q15, 32Q57, [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT], [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]

@article{hal-00881747,
     author = {Teleman, Andrei and Toma, Matei},
     title = {Holomorphic vector bundles on non-algebraic surfaces},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00881747}
}

Teleman, Andrei; Toma, Matei. Holomorphic vector bundles on non-algebraic surfaces. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00881747/