StatePolytope

Gröbner techniques for low-degree Hilbert stability Let V be an N+1-dimensional k-vector space, k an algebraically closed field. Hilbert stability of bicanonical models of curves of small genus with suitable large automorphism groups with respect to linearizations of fixed small degree is studied. A method is given for deducing the stability (with respect to SL(V)) of the Hilbert point of a subscheme X of ℙ(V) from a symbolic calculation of certain state polytopes. The method is implemented in the package StatePolytope in Macaulay2 based on the packages gfan and polymake. Several examples are treated among them the so–called Wiman curves (special hyperelliptic curves) and joins of Wiman curves.

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