Syzygies of Jacobian ideals and weighted homogeneous singularities

Abstract. Let V be a projective hypersurface having only isolated weighted homogeneous singularities. We show that the Koszul syzygies among the partial derivatives of an equation for V are exactly the syzygies vanishing on the singular locus subscheme of V . A positive answer to a question raised by Morihiko Saito and the first author is also given in this setting. We explain how our result can be used to improve the listing of Jacobian syzygies of a given degree by the computer algebra systems such as Singular, CoCoA or Macauley2.

• Type: Journal
• Year: 2016
• Where: JSC
• Authors: Alexandru Dimca, Gabriel Sticlaru
• Keywords: JSC 2016