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A computation of tight closure in diagonal hypersurfaces

Anurag K. Singh
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Abstract

In the ring R=K[X,Y,Z]/(X^3+Y^3+Z^3), where K is a field of prime characteristic p other than 3, determining the tight closure of the ideal (X^2, Y^2, Z^2)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[X_1,...,X_n]/(X_1^n + ... + X_n^n).

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Anurag K. Singh. 2002-09-18. A computation of tight closure in diagonal hypersurfaces. https://arxiv.org/abs/math/0209239

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