English

On linear differential equations with reductive Galois group

Algebraic Geometry 2012-03-02 v3

Abstract

Given a connection on a meromorphic vector bundle over a compact Riemann surface with reductive Galois group, we associate to it a projective variety. Connections such that their associated projective variety are curves can be classified, up to projective equivalence, using ruled surfaces. In particular, such a meromorphic connection is the pullbacks of a Standard connection. This extend a similar result by Klein for second-order ordinary linear differential equations to a broader class of equations.

Keywords

Cite

@article{arxiv.1007.4502,
  title  = {On linear differential equations with reductive Galois group},
  author = {Camilo Sanabria},
  journal= {arXiv preprint arXiv:1007.4502},
  year   = {2012}
}

Comments

v2 information on funding added v3 presentation rewritten, computational examples added

R2 v1 2026-06-21T15:53:08.158Z