2011/11/07 by Alexandru Dimca, Gabriel Sticlaru, Dimca, Alexandru +1 · 2 citations
Mathematics · #Geometry and complex manifolds #Holomorphic and Operator Theory #Commutative Algebra and Its Applications
paper · doi:10.48550/arxiv.1111.1533
We give sharp lower bounds for the degree of the syzygies involving the partial derivatives of a homogeneous polynomial defining a nodal hypersurface. The result gives information on the position of the singularities of a nodal hypersurface expressed in terms of defects or superabundances. The case of Chebyshev hypersurfaces is considered as a test for this result and leads to a potentially infinite family of nodal hypersurfaces having nontrivial Alexander polynomials.