An algorithm for construction of commuting ordinary differential operators by geometric data
type: Item
instance of: scholarly article
title: An algorithm for construction of commuting ordinary differential operators by geometric data
zbMATH Open document ID: 1387.14097
DOI: 10.1134/S1995080217060117
author: D. A. Pogorelov
author: Alexander Zheglov
published in: Lobachevskii Journal of Mathematics
publication date: 2018-03-02T00:00:00Z
review text: The aim of this paper is to give a description and program realization of an algorithm which produces explicit examples of commuting ordinary differential operators with rational coefficients by geometric spectral data consisting of a rational curve and a torsion free sheaf with some trivialization. The paper is organized as follows. The first section is an introduction to the subject. In Section 2 the authors give a survey on Schur pairs, geometric data and commuting differential operators to explain all theoretical ingredients they use in the algorithm and to make the paper self-contained. Section 3 contains the explanation of the first part of the algorithm. In particular, in this section they explain two ways of calculation Schur pairs from spectral data. The major new result is about direct images of torsion free sheaves (Any torsion free sheaf over a rational curve is the direct image of a torsion free rank one sheaf over another rational curve). The section also contains several examples of explicit Schur pairs. Section 4 contains a description of the algorithm. In Section 5 the authors give several test examples of computer calculations. In Appendix they give an overview of codes and procedures together with an estimate of their complexity.
reviewed by: Ahmed Lesfari
Mathematics Subject Classification ID: 14H70
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 13N10
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 37K10
zbMATH DE Number: 6846092
zbMATH Keywords: commuting ordinary differential operators
zbMATH Keywords: Krichever correspondence
zbMATH Keywords: Sato theory
Wikidata QID: Q115247380
MaRDI profile type: Publication
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full work available at URL: s1995080217060117
OpenAlex ID: W2769596997
description: scientific article; zbMATH DE number 6846092