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On vector bundles on algebraic surfaces and 0-cycles
| Content Provider | Scilit |
|---|---|
| Author | Ballico, E. |
| Copyright Year | 1993 |
| Description | Let X be an algebraic complex projective surface equipped with the euclidean topology and E a rank 2 topological vector bundle on X. It is a classical theorem of Wu ([Wu]) that E is uniquely determined by its topological Chern classes . Viceversa, again a classical theorem of Wu ([Wu]) states that every pair (a, b) ∈ (H (X, Z), Z) arises as topological Chern classes of a rank 2 topological vector bundle. For these results the existence of an algebraic structure on X was not important; for instance it would have been sufficient to have on X a holomorphic structure. In [Sch] it was proved that for algebraic X any such topological vector bundle on X has a holomorphic structure (or, equivalently by GAGA an algebraic structure) if its determinant line bundle has a holomorphic structure. It came as a surprise when Elencwajg and Forster ([EF]) showed that sometimes this was not true if we do not assume that X has an algebraic structure but only a holomorphic one (even for some two dimensional tori (see also [BL], [BF], or [T])). |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/58FB430CCFA4200943817FDC1E99DA15/S0027763000004402a.pdf/div-class-title-on-vector-bundles-on-algebraic-surfaces-and-0-cycles-div.pdf |
| Ending Page | 23 |
| Page Count | 5 |
| Starting Page | 19 |
| ISSN | 00277630 |
| e-ISSN | 21526842 |
| DOI | 10.1017/s0027763000004402 |
| Journal | Nagoya Mathematical Journal |
| Volume Number | 130 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1993-06-01 |
| Access Restriction | Open |
| Subject Keyword | Nagoya Mathematical Journal Applied Mathematics Vector Bundle Topological Vector |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
