Normal forms of one-dimensional quasihomogeneous complete intersections

A. G. Aleksandrov

Sbornik. Mathematics, Tome 45 (1983) no. 1, pp. 1-30

Résumé

In this paper the author presents an approach to the problem of classifying quasihomogeneous singularities, based on the use of simple properties of deformation theories of such singularities. By means of Grothendieck local duality the Poincaré series of the space of the first cotangent functor $T^1$ of a one-dimensional singularity is computed. Lists of normal forms and monomial bases of the spaces of $T^1$ are given for one-dimensional quasihomogeneous complete intersections with inner modality 0 and 1, and also with Milnor number less than seventeen. An adjacency diagram is constructed for all singularities that have been found. Bibliography: 33 titles.

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