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

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

2011-12-06

arxiv.org/abs/1112.1214v1

Mathematics

Differential Geometry

Scientific paper

In this paper, we propose one index $i_1(f)-i_2(f)$ which measures how well-behaved a given finitely determined multigerm $f: (\mathbb{K}^n,S)\to (\mathbb{K}^p,0)$ $(n\le p)$ 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?

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