On the classification of simple singularities in positive characteristic. The aim of the article is to describe the classification of simple isolated hypersurface singularities over a field of positive characteristic by certain invariants without computing the normal form. We also give a description of the algorithms to compute the classification which we have implemented in the Singular libraries classifyCeq.lib and classifyReq.lib.

References in zbMATH (referenced in 29 articles , 1 standard article )

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  1. Gunther, Joseph: Random hypersurfaces and embedding curves in surfaces over finite fields (2017)
  2. Burban, Igor; Gnedin, Wassilij: Cohen-Macaulay modules over some non-reduced curve singularities (2016)
  3. Greuel, Gert-Martin; Hong Duc Nguyen: Right simple singularities in positive characteristic (2016)
  4. Kalck, Martin; Yang, Dong: Relative singularity categories. I: Auslander resolutions. (2016)
  5. Białkowski, Jerzy; Erdmann, Karin; Skowroński, Andrzej: Periodicity of self-injective algebras of polynomial growth (2015)
  6. Ito, Hiroyuki; Schröer, Stefan: Wild quotient surface singularities whose dual graphs are not star-shaped (2015)
  7. Afzal, Deeba; Binyamin, Muhammad Ahsan; Janjua, Faira Kanwal: On the classification of simple singularities in positive characteristic (2014)
  8. Tyomkin, Ilya: On Zariski’s theorem in positive characteristic (2013)
  9. Araya, Tokuji; Iima, Kei-ichiro; Takahashi, Ryo: On the structure of Cohen-Macaulay modules over hypersurfaces of countable Cohen-Macaulay representation type (2012)
  10. Białkowski, Jerzy; Erdmann, Karin; Skowroński, Andrzej: Deformed mesh algebras of Dynkin type $\mathbb C_n$. (2012)
  11. Boubakri, Yousra; Greuel, Gert-Martin; Markwig, Thomas: Invariants of hypersurface singularities in positive characteristic (2012)
  12. Dugas, Alex: Periodicity of $d$-cluster-tilted algebras. (2012)
  13. Białkowski, Jerzy; Erdmann, Karin; Skowroński, Andrzej: Deformed preprojective algebras of generalized Dynkin type $\Bbb L_n$: classification and symmetricity. (2011)
  14. Ito, Hiroyuki: Deformation of a singularity of type $E_8$ and Mordell-Weil lattices in characteristic 2 (2010)
  15. Toda, Yukinobu; Yasuda, Takehiko: Noncommutative resolution, F-blowups and $D$-modules (2009)
  16. Yasuda, Takehiko: On monotonicity of F-blowup sequences (2009)
  17. Zhukov, I.B.: Iversen’s formula for the second Chern classes of regular surfaces in any characteristic (2008)
  18. Schröer, Stefan: Kummer surfaces for the self-product of the cuspidal rational curve (2007)
  19. Duc Tai Pho; Shimada, Ichiro: Unirationality of certain supersingular $K3$ surfaces in characteristic 5 (2006)
  20. Shimada, Ichiro: Singularities of dual varieties in characteristic 3 (2006)

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