Projective structures and projective bundles over compact Riemann surfaces

Details Projective structures and projective bundles over compact Riemann surfaces Projective structures and projective bundles over compact Riemann surfaces

2007-06-25

arxiv.org/abs/0706.3608v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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.

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