Giraldo Suárez, LuisGómez-Mont, X.Mardešic, P.2023-06-202023-06-2020080025-587410.1007/s00209-007-0262-9https://hdl.handle.net/20.500.14352/50107We introduce bilinear forms in a flag in a complete intersection local 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.engjournal articlehttp://www.springerlink.com/content/9777668l3584u182/fulltext.pdfhttp://www.springerlink.comrestricted access514.7Singularities of functions · Local algebra · Bilinear form · Index of vector fieldGeometría diferencial1204.04 Geometría Diferencial