A computation of tight closure in diagonal hypersurfaces
Abstract
In the ring R=K[X,Y,Z]/(X3+Y3+Z3), where K is a field of prime characteristic p other than 3, determining the tight closure of the ideal (X2, Y2, Z2)R had existed as a classic example of the difficulty involved in tight closure computations. We settle this question, compute the Frobenius closure of this ideal, and generalize these results to the diagonal hypersurfaces K[X1,...,Xn]/(X1n + ... + Xnn).
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