Symbolic squares in regular local rings (Q1273133)
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scientific article; zbMATH DE number 1229580
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Symbolic squares in regular local rings |
scientific article; zbMATH DE number 1229580 |
Statements
Symbolic squares in regular local rings (English)
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8 March 1999
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When \textit{D. Eisenbud} and \textit{B. Mazur} studied Kähler differentials [J. Reine Angew. Math. 488, 189-201 (1997; Zbl 0912.13010)], they posed a question: Let \((R, \mathfrak m)\) be a regular local ring and \(I\) an unmixed ideal in \(R\). When is it true that the symbolic power \(I^{(2)}\) is contained in \(\mathfrak m I\)? In the case where the characteristic of \(R\) is a positive prime, a counterexample was given by themselves. However there exists no counterexample in the case of characteristic \(0\). The present paper gives several classes of ideals, for example generically complete intersection, where the answer is ``yes'' in characteristic \(0\).
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symbolic square
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integral closure
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residual intersection
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Kähler differentials
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regular local ring
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complete intersection
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