Abstract

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,-mKF) ≠ 0, then S contains a Global Spherical Shell. We apply this last result to complete classification of bihermitian surfaces.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 639-670
Launched on MUSE
2006-05-24
Open Access
No
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