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Ideals of one-branch singularities of curves of the type W

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Ukrainian Mathematical Journal Aims and scope

We establish necessary and sufficient conditions for a one-branch singularity of the type W of a plane algebraic curve to have at most two-parameter families of ideals.

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References

  1. H. Jacobinski, “Sur les ordres commutatifs avec un nombre fini de r´eseaux ind´ecomposables,” Acta Math., 118, 1–31 (1961).

    Article  MathSciNet  Google Scholar 

  2. Yu. A. Drozd and A. V. Roiter, “Commutative rings with finitely many indecomposable integer-valued representations,” Izv. Akad. Nauk SSSR, Ser. Mat., 31, 783–798 (1967).

    MATH  MathSciNet  Google Scholar 

  3. G.-M. Greuel and H. Knörer, “Simple singularities in positive characteristic,” Math. Z., 203, 339–354 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  4. V. I. Arnold, S. M. Gusein-Zade, and A. N. Varchenko, Singularities of Differentiable Maps, Vol. 1, Birkhäuser, Boston (1985).

    Google Scholar 

  5. A. Schappert, “A characterization of strict unimodal plane curve singularities,” in: Singularities, Representation of Algebras and Vector Bundles, Springer, Berlin (1987), pp. 168–177.

    Chapter  Google Scholar 

  6. C. T. C. Wall, “Classification of unimodal isolated singularities of complete intersections,” Proc. Symp. Pure Math., 40, No. 2, 625–640 (1983).

    Google Scholar 

  7. Y. A. Drozd and G.-M. Greuel, “Cohen–Macaulay module type,” Compos. Math., 89, 315–338 (1993).

    MATH  MathSciNet  Google Scholar 

  8. Y. A. Drozd and G.-M. Greuel, “On Schappert’s characterization of strictly unimodal plane curve singularities,” in: Singularities: The Brieskorn Anniversary Volume, Birkhäuser (1998), pp. 3–26.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 9, pp. 1257–1266, September, 2009.

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Skuratovs’kyi, R.V. Ideals of one-branch singularities of curves of the type W . Ukr Math J 61, 1487–1498 (2009). https://doi.org/10.1007/s11253-010-0291-0

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  • DOI: https://doi.org/10.1007/s11253-010-0291-0

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