Pfaffian ideals of ladders
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.
scientific article; zbMATH DE number 1121680