Special birational structures on non-K\"ahler complex surfaces
Abstract
We investigate the following conjecture: all compact non-K\"ahler complex surfaces admit birational structures. After Inoue-Kobayashi-Ochiai, the remaining cases to study are essentially surfaces in class VII_0^+. In case of Kato surfaces with a cycle and one branch of rational curves we show that they have a special birational structure given by new normal forms of contracting germs in Cremona group Bir(P^2(C)). In particular all surfaces S with GSS and 0<b_2(S)<4 admit a birational structure. From the existence of a special birational structure we deduce meromorphic mappings from the universal cover of S to the projective plane which blow down an infinite number of rational curves.
Cite
@article{arxiv.1508.01900,
title = {Special birational structures on non-K\"ahler complex surfaces},
author = {Georges Dloussky},
journal= {arXiv preprint arXiv:1508.01900},
year = {2016}
}
Comments
36 pages, 2 figures, small corrections, corollary 2.9 modified, accepted in Journal de Math\'ematiques Pures et Appliqu\'ees