Minimal generation of ideals of algebraic varieties at points with multilinear tangent cones

Abstract

Let $$A$$ be the local ring, at a singular isolated point $$P$$ of an affine irreducible algebraic variety $$V$$ , with regular normalization. Let $$\mathfrak p$$ be the prime ideal of $$A$$ corresponding to $$V$$ . In this paper we study the minimal number of generators of $$\mathfrak p$$ , when the projectivized tangent cone of $$V$$ at $$P$$ is multilinear (that is union of linear varieties) and has maximal rank.