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On surfaces of class VII+0 with numerically anticanonical divisor
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 128, Number 3, June 2006
- pp. 639-670
- 10.1353/ajm.2006.0021
- Article
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We consider minimal compact complex surfaces S with Betti numbers b1 = 1 and n = b2 > 0. A theorem of Donaldson gives n exceptional line bundles. We prove that if in a deformation, these line bundles have sections, S is a degeneration of blown-up Hopf surfaces. Besides, if there exists an integer m ≥ 1 and a flat line bundle F such that H0(S,-mK ⊗ F) ≠ 0, then S contains a Global Spherical Shell. We apply this last result to complete classification of bihermitian surfaces.