Algorithmetical aspects of the problem of classifying multi-projections of Veronesian varieties. (English) Zbl 0699.14060
Let W be a projection of a Veronesian variety. 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.
Reviewer: C.-P.Ionescu
MSC:
| 14M05 | Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) |
| 14-04 | Software, source code, etc. for problems pertaining to algebraic geometry |
| 14N05 | Projective techniques in algebraic geometry |
| 13H10 | Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) |
Keywords:
classifying projections of a Veronesian variety; arithmetically Cohen- Macaulay; arithmetically BuchsbaumCitations:
Zbl 0135.211References:
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