NORMAL HILBERT COEFFICIENTS AND ELLIPTIC IDEALS IN NORMAL TWO-DIMENSIONAL SINGULARITIES
抄録
<jats:title>Abstract</jats:title><jats:p>Let <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0027763022000058_inline1.png" /><jats:tex-math> $(A,\mathfrak m)$ </jats:tex-math></jats:alternatives></jats:inline-formula> be an excellent two-dimensional normal local domain. In this paper, we study the elliptic and the strongly elliptic ideals of <jats:italic>A</jats:italic> with the aim to characterize elliptic and strongly elliptic singularities, according to the definitions given by Wagreich and Yau. In analogy with the rational singularities, in the main result, we characterize a strongly elliptic singularity in terms of the normal Hilbert coefficients of the integrally closed <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0027763022000058_inline2.png" /><jats:tex-math> $\mathfrak m$ </jats:tex-math></jats:alternatives></jats:inline-formula>-primary ideals of <jats:italic>A</jats:italic>. Unlike <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0027763022000058_inline3.png" /><jats:tex-math> $p_g$ </jats:tex-math></jats:alternatives></jats:inline-formula>-ideals, elliptic ideals and strongly elliptic ideals are not necessarily normal and necessary, and sufficient conditions for being normal are given. In the last section, we discuss the existence (and the effective construction) of strongly elliptic ideals in any two-dimensional normal local ring.</jats:p>
収録刊行物
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- Nagoya Mathematical Journal
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Nagoya Mathematical Journal 248 779-800, 2022-03-10
Cambridge University Press (CUP)
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詳細情報 詳細情報について
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- CRID
- 1360298339675282688
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- ISSN
- 21526842
- 00277630
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- データソース種別
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