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arXiv · 1104.3070

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

Duco van Straten·Thorsten Warmt
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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 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.

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Duco van Straten, Thorsten Warmt. 2011-04-15. Gorenstein-duality for one-dimensional almost complete intersections-with an application to non-isolated real singularities. https://doi.org/10.1017/s0305004114000504

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