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Article Dans Une Revue Journal of Symbolic Computation Année : 2016

Syzygies of Jacobian ideals and weighted homogeneous singularities

Alexandru Dimca
Gabriel Sticlaru
  • Fonction : Auteur

Résumé

Let V be a projective hypersurface having only isolated singularities. We show that these singularities are weighted homogeneous if and only if the Koszul syzygies among the partial derivatives of an equation for V are exactly the syzygies with a generic first component vanishing on the singular locus subscheme of V. This yields in particular a positive answer in this setting to a question raised by Morihiko Saito and the first author. Finally we explain how our result can be used to improve the listing of jacobian syzygies of a given degree by a computer algebra system such as Singular, CoCoA or Macaulay2

Dates et versions

hal-01141823 , version 1 (13-04-2015)

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Alexandru Dimca, Gabriel Sticlaru. Syzygies of Jacobian ideals and weighted homogeneous singularities. Journal of Symbolic Computation, 2016, 74, pp.627-634. ⟨10.1016/j.jsc.2015.11.003⟩. ⟨hal-01141823⟩
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