Syzygies of Jacobian ideals and defects of linear systems
Abstract
Our main result describes the relation between the syzygies involving the first order partial derivatives f0,...,fn of a homogeneous polynomial f∈ [x0,...xn] and the defect of the linear systems vanishing on the singular locus subscheme f=V(f0,...,fn) of the hypersurface D:f=0 in the complex projective space n, when D has only isolated singularities.
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