Normal Reduction Numbers for Normal Surface Singularities with Application to Elliptic Singularities of Brieskorn Type

  • Tomohiro Okuma
  • Kei-ichi WatanabeEmail author
  • Ken-ichi Yoshida


In this paper, we give a formula for normal reduction number of an integrally closed \(\mathfrak m\)-primary ideal of a two-dimensional normal local ring \((A,\mathfrak m)\) in terms of the geometric genus pg(A) of A. Also, we compute the normal reduction number of the maximal ideal of Brieskorn hypersurfaces. As an application, we give a short proof of a classification of Brieskorn hypersurfaces having elliptic singularities.


Normal reduction number Geometric genus Hypersurface of Brieskorn type 

Mathematics Subject Classification (2010)

13B22 Secondary 14B05 14J17 


Funding Information

This work was partially supported by JSPS Grant-in-Aid for Scientific Research (C) Grant Nos., 25400050, 26400053, 17K05216.


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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Tomohiro Okuma
    • 1
  • Kei-ichi Watanabe
    • 2
    Email author
  • Ken-ichi Yoshida
    • 2
  1. 1.Department of Mathematical Sciences, Faculty of ScienceYamagata UniversityYamagataJapan
  2. 2.Department of Mathematics, College of Humanities and SciencesNihon UniversityTokyoJapan

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