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 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.
- Publication:
-
Mathematical Proceedings of the Cambridge Philosophical Society
- Pub Date:
- March 2015
- DOI:
- 10.1017/S0305004114000504
- arXiv:
- arXiv:1104.3070
- Bibcode:
- 2015MPCPS.158..249V
- Keywords:
-
- Mathematics - Algebraic Geometry;
- 14B05;
- 14J17;
- 13H10;
- 32S25
- E-Print:
- Math. Proc. Camb. Phil. Soc. 158 (2015) 249-268