On the dimension of systems of algebraic difference equations

Michael Wibmer

On the dimension of systems of algebraic difference equations

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arxiv 2004.01596 v2 pith:MSKWEK77 submitted 2020-04-03 math.AG math.AC

Michael Wibmer This is my paper

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keywords dimensiondifferencealgebraicequationsnotionsolutioncoveringdegrees

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We introduce a notion of dimension for the solution set of a system of algebraic difference equations that measures the degrees of freedom when determining a solution in the ring of sequences. This number need not be an integer, but, as we show, it satisfies properties suitable for a notion of dimension. We also show that the dimension of a difference monomial is given by the covering density of its set of exponents.

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