Fragmented deformations of primitive multiple curves

Jean-Marc Drézet (1)

1 IMJ - Institut de Mathématiques de Jussieu

A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that 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.

Mots clés: Primitive multiples curves; deformations

Domaines: Géométrie algébrique [math.AG]

Jean-Marc Drézet. Fragmented deformations of primitive multiple curves. Central European Journal of Mathematics, 2013, 11 (12), pp.2106-2137. ⟨hal-00742545v2⟩