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Self-linked curve singularities

  • Jürgen Herzog (a1) and Bernd Ulrich (a2)

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Let S be a three-dimensional regular local ring and let I be a prime ideal in S of height two. This paper is motivated by the question of when I is a set-theoretic complete intersection and when the symbolic Rees algebra S(I) = ⊕ n≥0 I(n)tn is Noetherian. The connection between the two problems is given by a result of Cowsik which says that the Noetherian property of S(I) implies that I is a set-theoretic complete intersection ([1]).

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References

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[1] Cowsik, R., Symbolic powers and number of defining equations, in “Algebra and its applications (New Delhi, 1981)”, Lecture Notes in Pure and Appl. Math., Vol. 91, Dekker, New York, 1984, 1314.
[2] Cowsik, R. and Nori, , On the fibres of blowing-up, J. Indian Math. Soc., 40 (1976), 217222.
[3] Eliahou, S., Symbolic powers of monomial curves, preprint.
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Self-linked curve singularities

  • Jürgen Herzog (a1) and Bernd Ulrich (a2)

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