Computing Tjurina stratifications of \(\mu \)-constant deformations via parametric local cohomology systems

  • Katsusuke NabeshimaEmail author
  • Shinichi Tajima
Original Paper


Algebraic local cohomology classes associated with parametric semi-quasihomogeneous hypersurface isolated singularities are considered in the context of symbolic computation. The motivations for this paper are computer calculations of complete lists of Tjurina numbers of semi-quasihomogeneous polynomials with isolated singularity. A new algorithm, that utilizes parametric local cohomology systems, is proposed to compute Tjurina stratifications associated with \(\mu \)-constant deformations of weighted homogeneous isolated singularities. The resulting algorithm gives in particular a suitable decomposition of the parameter space depending on the structure of the parametric local cohomology systems. An efficient algorithm of computing parametric standard bases of relevant ideals is also given as an application of parametric local cohomology systems.


Semi-quasihomogeneous isolated singularity Local cohomology \(\mu \)-constant deformation Standard bases Tjurina algebra 

Mathematics Subject Classification

13D45 32C37 13J05 32A27 



This work has been partly supported by JSPS Grant-in-Aid for Young Scientists (B) (No.15K17513) and Grant-in-Aid for Scientific Research (C) (No.15K04891).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Graduate School of Science and TechnologyTokushima UniversityTokushimaJapan
  2. 2.Graduate School of Pure and Applied SciencesUniversity of TsukubaTsukubaJapan

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