Desingularization Explains Order-Degree Curves for Ore Operators
arXiv:1301.0917
Abstract
Desingularization is the problem of finding a left multiple of a given Ore operator in which some factor of the leading coefficient of the original operator is removed. An order-degree curve for a given Ore operator is a curve in the -plane such that for all points above this curve, there exists a left multiple of order and degree of the given operator. We give a new proof of a desingularization result by Abramov and van Hoeij for the shift case, and show how desingularization implies order-degree curves which are extremely accurate in examples.