We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors embedding weights in projective space to ${\sim}1$ mean absolute error, whilst classifiers dimension and Gorenstein index $>90\%$ accuracy with ${\sim}0.5\%$ standard error. Binary random forest managed distinguish whether the underlying HS describes a complete intersec...

We use the results of our paper p-Fractals and power series I—Some 2 variable results (Journal of Algebra 280, 2004, pp. 505–536) to prove the rationality of the Hilbert-Kunz series of a large family of power series, including those of the form ∑ i fi(xi, yi), where the fi(xi, yi) are power series with coefficients in a finite field. The methods are effective, as we illustrate with examples. In...