Degrevlex Gröbner bases of generic complete intersections.
A generic standard graded algebra is an algebra \(K[X_1,\dots,X_n]/(g_1,\dots, g_m)\) where \(g_1,\dots,g_m\) are generic polynomials over a field \(K\). Let \(A\) be a generic algebra which is a complete intersection. Starting from the Hilbert Samuel function of \(A\), which is well known, the author studies the Hilbert-Samuel function of \(A\) refined by an \((\ell)\)-adic filtration, \(\ell\) being a linear form. As an application he obtains a structure theorem which describes the stairs of such algebras with respect to the degree reverse-lexicographic order. Moreover a conjecture is stated on the Gröbner bases of \(A\) with respect to the degree reverse-lexicographic order, and it is proved in some special cases.
scientific article; zbMATH DE number 1917888
scientific article