On linear differential equations with reductive Galois group

JOURNAL OF ALGEBRA

卷:408

Article

Sanabria Malagon, Camilo

关键词: Ordinary linear differential equations;    Differential Galois theory;    Differential algebra;    Reductive groups;    Meromorphic connections;    Invariants;    First integrals;    Projective equivalence;    Pullbacks;   

DOI  :  10.1016/j.jalgebra.2014.02.035

来源: Elsevier

【 摘 要 】

Given a connection on a meromorphic vector bundle over a compact Riemann surface with reductive differential Galois group, we associate to it a projective variety. Connections such that their associated projective variety is curves can be classified, up to projective equivalence, using ruled surfaces. In particular, such a meromorphic connection is the pullback of a standard connection. This extends a similar result by Klein for second-order ordinary linear differential equations to a broader class of equations. (C) 2014 Elsevier Inc. All rights reserved.

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