Vector fields liftable over finitely determined multigerms of corank at most one

2011/12/06 by Takashi Nishimura, Nishimura, Takashi
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1112.1214

Abstract

In this paper, we propose one index i₁(f)-i₂(f) which measures how well-behaved a given finitely determined multigerm f: (\mathbbKⁿ,S)→ (\mathbbK^p,0) (n≤ p) of corank at most one is from the viewpoint of liftable vector fields; and we answer the following problems when the index indicates that the given multigerm f is best-behaved. 1) When is the module of vector fields liftable over f finitely generated? 2) How can we characterize the minimal number of generators when the module of vector fields liftable over f is finitely generated? 3) How can we calculate the minimal number of generators when the module of vector fields liftable over f is finitely generated? 4) How can we construct generators when the module of vector fields liftable over f is finitely generated?

Citations

• The general type of singularity of a set of 2n−1 smooth functions of n variables

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