@**techreport**{RISC4635,author = {Maximilian Jaroschek and Manuel Kauers and Shaoshi Chen and Michael F. Singer},

title = {{Desingularization Explains Order-Degree Curves for Ore Operators}},

language = {english},

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 $(r,d)$-plane
such that for all points $(r,d)$ above this curve, there exists a left
multiple of order~$r$ and degree~$d$ 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.
},

number = {1301.0917},

year = {2013},

institution = {ArXiv},

length = {8}

}