On the value-semigroup of a simple complete ideal in a two-dimensional regular local ring

S. Greco; K. Kiyek

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arXiv · 0712.4329

On the value-semigroup of a simple complete ideal in a two-dimensional regular local ring

S. Greco·K. Kiyek

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Abstract

Let R be a two-dimensional regular local ring with maximal ideal \mathfrak m, and let \wp be a simple complete \mathfrak m-primary ideal which is residually rational. Let R_0:= R\subsetneqq ...\subsetneqq R_r be the quadratic sequence associated to \wp, let Γ_\wp be the value-semigroup associated to \wp, and let ((e_j(\wp))_{0\leq j\leq r} be the multiplicity sequence of \wp. We associate to \wp a sequence of natural integers, the formal characteristic sequence of \wp, and we show that the value-semigroup, the multiplicity sequence and the formal characteristic sequence are equivalent data. Furthermore, we give a new proof that Γ_\wp is symmetric, and give a formula for c_\wp, the conductor of Γ_\wp, in terms of entries of the Hamburger-Noether tableau of \wp.

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S. Greco, K. Kiyek. 2007-12-28. On the value-semigroup of a simple complete ideal in a two-dimensional regular local ring. https://arxiv.org/abs/0712.4329

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