Pfaffian ideals of ladders. (English) Zbl 0899.13014
Let \(X\) be a skew symmetric matrix of indeterminates over a field \(K\). A ladder \(Y\) of \(X\) is a union of a set of skew symmetric submatrices of \(X\). This paper concerns the study of the ideal \(I_{2t} (Y)\) of \(K[Y]\) generated by the \(2t\)-Pfaffians of \(Y\) and its coordinate ring \(R_{2t} (Y)= K[Y]/I_{2t} (Y)\). The author proves that the set of \(2t\)-Pfaffians of \(Y\) is a Gröbner basis of \(I_{2t} (Y)\) and obtains as a consequence that \(R_{2t}(Y)\) is a Cohen-Macaulay normal domain, moreover she characterizes those which are Gorenstein rings.
Reviewer: M.Morales (Saint-Martin-d’Heres)
MSC:
| 13C40 | Linkage, complete intersections and determinantal ideals |
| 13P10 | Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |
| 13H10 | Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) |
| 13C14 | Cohen-Macaulay modules |
| 13G05 | Integral domains |
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