no. 4
Topological triviality of versal unfoldings of complete intersections
Annales de l'Institut Fourier, Tome 34 (1984) no. 4, pp. 225-251.

On obtient des conditions algébriques et géométriques qui impliquent la trivialité topologique des déploiements versels des intersections complètes quasi-homogènes le long des sous-espaces correspondant aux déformations de poids maximal. On les applique : à certaines familles infinies de singularités de surfaces de C 4 commençant par des singularités unimodulaires exceptionnelles, à l’intersection de paires de quadriques, et à quelques singularités de courbes.

Ces conditions algébriques sont reliées à l’opération d’adjoindre une puissance qui généralise aux intersections complètes la construction de Thom-Sabastiani. On démontre un résultat de dualité qui relie le fait que l’algèbre jacobienne de f est de Gorenstein et le fait que N ˜(F) * est principal, c’est-à-dire engendré par un élément (ici on obtient F en adjoignant une puissance à f, N ˜(F) * désigne le dual de l’espace des déformations infinitésimales non-triviales).

We obtain algebraic and geometric conditions for the topological triviality of versal unfoldings of weighted homogeneous complete intersections along subspaces corresponding to deformations of maximal weight. These results are applied: to infinite families of surface singularities in C 4 which begin with the exceptional unimodular singularities, to the intersection of pairs of generic quadrics, and to certain curve singularities.

The algebraic conditions are related to the operation of adjoining powers, a generalization for complete intersections of a special form of the Thom-Sebastiani operation. A duality result is proven which relates the Jacobian algebra of f being Gorenstein with N ˜(F) * being principal, i.e. generated by one element (here F is obtained from f by adjoining powers, and N ˜(F) * is the dual of the space of non-trivial infinitesimal deformations.

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     title = {Topological triviality of versal unfoldings of complete intersections},
     journal = {Annales de l'Institut Fourier},
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Damon, James. Topological triviality of versal unfoldings of complete intersections. Annales de l'Institut Fourier, Tome 34 (1984) no. 4, pp. 225-251. doi : 10.5802/aif.995. https://aif.centre-mersenne.org/articles/10.5802/aif.995/

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