A property deducible from the generic initial ideal Original Research Article

Let Sd be the vector space of monomials of degree d in the variables x1,…,xs. For a subspace V subset of or equal to Sd which is in general coordinates, consider the subspace gin(V) subset of or equal to Sd generated by initial monomials of polynomials in V for the revlex order. We address the question of what properties of V may be deduced from gin(V). This is an approach for understanding what algebraic or geometric properties of a homogeneous ideal I subset of or equal to k[x1,…,xs] that may be deduced from its generic initial ideal gin(I).