On the syzygies and Alexander polynomials of nodal hypersurfaces

Details On the syzygies and Alexander polynomials of nodal hypersurfaces On the syzygies and Alexander polynomials of nodal hypersurfaces

2011-11-07

arxiv.org/abs/1111.1533v2

Mathematics

Algebraic Geometry

The second version: some minor changes made and Example 4.3 involving Kummer surfaces with 16 nodes added

Scientific paper

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.

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