Lipschitz Trivial Values of Polynomial Mappings

We prove that a polynomial mapping $$f:{{\mathbb {K}}^{n}}\rightarrow {\mathbb {K}}^{p}$$ , where $${\mathbb {K}}=\mathbb {R}$$ or $$\mathbb {C}$$ attains Lipschitz trivial value $$\mathbf{c}$$ if and only there exist $$g:{\mathbb {K}}^m \rightarrow for which the is regular of properness, linear surjective projection $$\pi :{{\mathbb {K}}^m$$ such $$f = g\circ \pi $$ . The integer m {K}}$$ -codimension accumulation set at infinity level $$f^{-1}(\mathbf{c})$$ in hyperplane infinity. In complex case, it equivalent to require g be generically finite dominant. Last, we show this result cannot extend rational mappings over $${{\mathbb {K}}^{n}}$$