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arXiv · 1210.3920

Fragmented deformations of primitive multiple curves

J. -M. Drezet
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Abstract

A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that the associated reduced curve Y_red is smooth. The subject of this paper is the study of deformations of Y in curves with smooth irreducible components, when the number of components is maximal (it is then the multiplicity n of Y). We are particularly interested in deformations in n disjoint smooth irreducible components, which are called fragmented deformations. We describe them completely. We give also a characterization of primitive multiple curves having a fragmented deformation.

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J. -M. Drezet. 2012-10-15. Fragmented deformations of primitive multiple curves. https://arxiv.org/abs/1210.3920

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