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 $V_m$, $m\ge 0$. 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 $\Gamma (f)$.

arXiv commentFinal version to appear in the Journal of Algebra