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

Published online by Cambridge University Press:  16 December 2014

DUCO VAN STRATEN  and
THORSTEN WARMT
DUCO VAN STRATEN
Affiliation:
e-mail: straten@mathematik.uni-mainz.de
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Abstract

We give a generalisation of the duality of a zero-dimensional complete intersection for the case of one-dimensional almost complete intersections, which results in a 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/Jf to the Euler characteristic of the positive and negative Milnor fibre, generalising the result for isolated critical points. An application to real curves in ℙ2(ℝ) of even degree is given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 158 , Issue 2 , March 2015 , pp. 249 - 268
Copyright
Copyright © Cambridge Philosophical Society 2014 

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