Alexandru Dimca: Syzygies of Jacobian ideals and defects of linear systems, p.191-203

Abstract:

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.

Key Words: Projective hypersurfaces, singularities, global Milnor algebra, syzygies, saturation of an ideal.

2000 Mathematics Subject Classification: Primary: 14B05;
Secondary: 13D40, 14C20, 13D02.

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