Algorithmetical aspects of the problem of classifying multi-projections of Veronesian varieties (Q912943)

Let W be a projection of a Veronesian variety. \textit{W. Gröbner} [Arch. Math. 16, 257-264 (1965; Zbl 0135.211)] showed that W can have imperfect defining prime ideals and posed the problem of classifying such projections. Here it is shown that, in the simplicial case, to check if such a projection is arithmetically Cohen-Macaulay or arithmetically Buchsbaum, one needs only finitely many operations. Then a practical criterion for a class of such projections to be arithmetically Cohen- Macaulay or arithmetically Buchsbaum is given. Finally, an upper bound for the difference between the Buchsbaum invariant and the so-called length of its associated semigroup ideal is obtained.