2017
DOI: 10.1215/ijm/1534924827
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Cohomology of ideals in elliptic surface singularities

Abstract: We introduce the the normal reduction number of twodimensional normal singularities and prove that elliptic singularity has normal reduction number two. We also prove that for a two-dimensional normal singularity which is not rational, it is Gorenstein and its maximal ideal is a pg-ideal if and only if it is a maximally elliptic singularity of degree 1.

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Cited by 8 publications
(12 citation statements)
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“…Remark 4.1.3. Using the relevant exact sequences one verifies that n 0 (Z, L) = min{n ≥ 0 : [O17,Lemma 3.6].…”
Section: Stability Bound Formentioning
confidence: 99%
See 2 more Smart Citations
“…Remark 4.1.3. Using the relevant exact sequences one verifies that n 0 (Z, L) = min{n ≥ 0 : [O17,Lemma 3.6].…”
Section: Stability Bound Formentioning
confidence: 99%
“…One has the following relations between the 'stabilized dimensions'. By [O17,Remark 3.8] or [NNI,Th. 6.1.9] we know that for L without fixed components lim n→∞ h 1 (Z,…”
Section: Stability Bound Formentioning
confidence: 99%
See 1 more Smart Citation
“…Okuma proved in [Ok,Theorem 3.3] that if A is an elliptic singularity, then r(A). For the definition of elliptic singularity we refer to [W, page 428] or [Ok,Definition 2.1].…”
Section: Elliptic and Strongly Elliptic Idealsmentioning
confidence: 99%
“…Okuma proved in [Ok,Theorem 3.3] that if A is an elliptic singularity, then r(A). For the definition of elliptic singularity we refer to [W, page 428] or [Ok,Definition 2.1]. We investigate the integrally closed m-primary ideals such that r(I) = 2 with the aim to characterize elliptic singularities.…”
Section: Elliptic and Strongly Elliptic Idealsmentioning
confidence: 99%