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Mathematische Zeitschrift

, Volume 260, Issue 1, pp 77–91 | Cite as

Flags in zero dimensional complete intersection algebras and indices of real vector fields

  • L. GiraldoEmail author
  • X. Gómez-Mont
  • P. Mardešić
Article

Abstract

We introduce bilinear forms in a flag in a complete intersection local \(\mathbb {R}\) -algebra of dimension 0, related to the Eisenbud–Levine, Khimshiashvili bilinear form. We give a variational interpretation of these forms in terms of Jantzen’s filtration and bilinear forms. We use the signatures of these forms to compute in the real case the constant relating the GSV-index with the signature function of vector fields tangent to an even dimensional hypersurface singularity, one being topologically defined and the other computable with finite dimensional commutative algebra methods.

Keywords

Singularities of functions Local algebra Bilinear form Index of vector field 

Mathematics Subject Classification (2000)

58K45 58K05 13H10 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Dep. MatemáticasUniversidad de CádizPuerto RealSpain
  2. 2.Dep. Geometría y Topología, F. MatemáticasUniversidad Complutense de MadridMadridSpain
  3. 3.CIMATGuanajuatoMexico
  4. 4.Institut de Mathématiques de Bourgogne, U.M.R. 5584 du C.N.R.S.Université de BourgogneDijon CedexFrance

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