Projective structures and projective bundles over compact Riemann surfaces
Classical Analysis and ODEs
2007-06-26 v1 Algebraic Geometry
Differential Geometry
Abstract
A projective structure on a compact Riemann surface X of genus g is given by an atlas with transition functions in PGL(2,C). Equivalently, a projective structure is given by a projective sl(2,C)-bundle over X equipped with a section s and a foliation F which is both transversal to the fibers and the section s. From this latter geometric bundle picture, we survey on classical problems and results on projective structures. We will give a complete description of projective (actually affine) structures on the torus with an explicit versal family of foliated bundle picture.
Cite
@article{arxiv.0706.3608,
title = {Projective structures and projective bundles over compact Riemann surfaces},
author = {Frank Loray and David Marìn},
journal= {arXiv preprint arXiv:0706.3608},
year = {2007}
}