On surfaces of class VII_0^+ with numerically anticanonical divisor
Complex Variables
2007-05-23 v3 Differential Geometry
Abstract
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.
Cite
@article{arxiv.math/0406387,
title = {On surfaces of class VII_0^+ with numerically anticanonical divisor},
author = {G. Dloussky},
journal= {arXiv preprint arXiv:math/0406387},
year = {2007}
}
Comments
31 pages, revised version, statement of thm 3.44 corrected, proof not changed. Accepted in Am. J. of Math