Flags in zero dimensional complete intersections and indices of real vector fields

Details Flags in zero dimensional complete intersections and indices of real vector fields Flags in zero dimensional complete intersections and indices of real vector fields

2006-12-11

arxiv.org/abs/math/0612275v2

Mathematics

Algebraic Geometry

17 pages. v2: Some changes in the introduction. A few typos corrected. To appear in Mathematische Zeitschrift

Scientific paper

10.1007/s00209-007-0262-9

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 by finite dimensional commutative algebra methods.

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