Syzygies of Jacobian ideals and defects of linear systems

By Alexandru Dimca. 2012

55 citations recorded by the source corpus.

Our main result describes the relation between the syzygies involving the first order partial derivatives $f_0,...,f_n$ of a homogeneous polynomial $f\in \C[x_0,...x_n]$ and the defect of the linear systems vanishing on the singular locus subscheme $\Sigma_f=V(f_0,...,f_n)$ of the hypersurface $D:f=0$ in the complex projective space $\PP^n$, when $D$ has only isolated singularities.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f7be0a31c91d127510d4815674a0572bc16e7630

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In Algebra and Number Theory

1. Alexandru Dimca
2. E. Sernesi
3. Gabriel Sticlaru
4. F. Catanese

In Geometry and Topology

1. Alexandru Dimca
2. E. Sernesi
3. Gabriel Sticlaru
4. F. Catanese

Citations in the corpus

• The local cohomology of the Jacobian ring (2013, background): “Additional interesting informations concerning the syzygies of (f0, f1, f2) for a singular plane curve are in [11].”
• Koszul Complexes and Pole Order Filtrations (2011, result): “A similar result for hypersurfaces D having arbitrary isolated singularities is obtained in [13].”