Combinatorial differential algebra of xp. (January 2023) - Ait El Manssour, Rida; Sattelberger, Anna-Laura
Abstract: We link n -jets of the affine monomial scheme defined by x p to the stable set polytope of some perfect graph. We prove that, as p varies, the dimension of the coordinate ring of a certain subscheme of the scheme of n -jets as a C -vector space is a polynomial of degree n + 1, namely the Ehrhart polynomial of the stable set polytope of that graph. One main ingredient for our proof is a result of Zobnin who determined a differential Gröbner basis of the differential ideal generated by x p . We generalize Zobnin's result to the bivariate case. We study ( m, n ) -jets, a higher-dimensional analog of jets, and relate them to regular unimodular triangulations.