Gorenstein-duality for one-dimensional almost complete intersections-with an application to non-isolated real singularities

Details Gorenstein-duality for one-dimensional almost complete intersections-with an application to non-isolated real singularities Gorenstein-duality for one-dimensional almost complete intersections-with an application to non-isolated real singularities

2011-04-15

arxiv.org/abs/1104.3070v1

Mathematics

Algebraic Geometry

Scientific paper

We give a generalization of the duality of a zero-dimensional complete intersection to the case of one-dimensional almost complete intersections, which results in a {\em Gorenstein module} $M=I/J$. In the real case the resulting pairing has a signature, which we show to be constant under flat deformations. In the special case of a non-isolated real hypersurface singularity $f$ with a one-dimensional critical locus, we relate the signature on the jacobian module $I/J_f$ to the Euler characteristic of the positive and negative Milnor fibre, generalising the result for isolated critical points. An application to real curves in $\P^2(\R)$ of even degree is given.

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