Title: Gorenstein-duality for one-dimensional almost complete intersections – with an application to non-isolated real singularities
Abstract: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...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 $¶^2(\R)$ of even degree is given.Read More