Deforming spaces of m-jets of hypersurfaces singularities

Abstract: Let $\mathbb{K}$ be an algebraically closed field of characteristic zero, and $V$ a hypersurface defined by an irreducible polynomial $f$ with coefficients in $\mathbb{K}$ . In this article we prove that an Embedded Deformation of $V$ which admits a Simultaneous Embedded Resolution induces, under certain mild conditions, a deformation of the reduced scheme associated to the space of $m$-jets $V_m$, $m\geq 0$. An example of an Embedded Deformation of $V$ which admits a Simultaneous Embedded Resolution is a $\Gamma(f)$-deformation of $V$, where $V$ has at most one isolated singularity, and $f$ is non degenerate with respect to the Newton Boundary $\Gamma(f)$.