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Families of m-jet spaces and arc spaces. Let V be an algebraic varietydefined over an algebraically closed field of characteristic zero. The m-jetspaces and the arc space provide the information on the geometry of the varietyV, therefore it is natural to ask the following questions: When will adeformation of V induce a deformation of the m-jet spaces and the arc space? Ifone considers a deformation of V which admits a flat simultaneous resolution,how will the image of the Nash application vary? In section 3 some partialanswers to these questions can be found. In section 4 two families ofhypersurfaces of the 4-dimensional affine space are shown in which the Nashapplication is bijective. What's more, in each case a desingularization inwhich all the irreducible components of the exceptional fiber are essentialdivisors is explicitly given. It is important to note that very few examples ofthis type are found in the literature.

Familles d'espaces de m-jets et d'espaces d'arcs