Polynomial subalgebras in two dimensions

In this project we look at subalgebras of the polynomial ring i two variables $LaTeX: \mathbb{K}[x,y]$ $\mathbb{K}[x,y]$ of low codimension. To such a subalgebra is associatied a finite set of points in $LaTeX: \mathbb{K}^2$ $\mathbb{K}^2$ called the Spectrum. Polynomials belong to the subalgebra if and only if they satisfy a (small) number of conditions on the polynomial and some of its directional derivatives in the spectral points. We want to classify such subalgebras.

Contact: Anna Torstensson (anna.torstensson@math.lth.se)