Syzygies of Jacobian ideals and weighted homogeneous singularities. (May 2016)

• Record Type: Journal Article
• Authors: Dimca, Alexandru; Sticlaru, Gabriel
• Is Part Of: Journal of symbolic computation. Volume 74(2016)
• Page Start: 627
• Page End: 634
• Publication Date: 2016-05
• Subjects: primary 14J70 13D02 -- secondary 14B05; Projective hypersurfaces -- Weighted homogeneous singularities -- Syzygies; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.11.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: 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.