Schwarz maps of algebraic linear ordinary differential equations

Malagón, Camilo Sanabria

doi:10.1016/j.jde.2017.08.002

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Cited by 4 publications

(2 citation statements)

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“…The present paper is mainly concerned with (i). It clarifies and extends work of [Ber,S1,S2,S3]. Moreover we propose new methods and examples for (i) related to a theorem of Compoint [C, B] concerning invariants.…”

Section: Introductionmentioning

confidence: 57%

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Linear differential equations with finite differential Galois group

2020

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For a differential operator L of order n over C(z) with a finite (differential) Galois group G ⊂ GL(C n ), there is an algorithm, by M. van Hoeij and J.-A. Weil, which computes the associated evaluation of the invariants ev :The procedure proposed here does the opposite: it uses a theorem of E. Compoint and computes the operator L from a given evaluation h. Moreover it solves a part of the inverse problem of producing L for a given representation of a finite group G. Another part considered here, is finding irreducible G-invariant curves Z ⊂ P(C n ) with Z/G of genus zero and constructing evaluations from this. The theory developed here is illustrated by various examples, and relates to and continues classical work of H.

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Section: Introductionmentioning

confidence: 57%

“…This method was refined in [vdP-U]. Klein's theorem is generalized in, e.g., [Ber,S1,S2,S3]. For (ii) there are many papers [S-U, Ho, H-W].…”

Section: Introductionmentioning

confidence: 99%