On surfaces of class VII_0^+ with numerically anticanonical divisor

Details On surfaces of class VII_0^+ with numerically anticanonical divisor On surfaces of class VII_0^+ with numerically anticanonical divisor

2004-06-19

arxiv.org/abs/math/0406387v3

Mathematics

Complex Variables

31 pages, revised version, statement of thm 3.44 corrected, proof not changed. Accepted in Am. J. of Math

Scientific paper

We consider minimal compact complex surfaces S with Betti numbers b_1=1 and n=b_2>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>0 and a flat line bundle F such that -mK\otimes F has nontrivial sections, then S contains a Global Spherical Shell. We apply this last result to complete classification of bihermitian surfaces.

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