A Remark on Polynomial Mappings from Cⁿ to C^n-1 and an Application of the Software Maple in Research

Abstract

In [1], we construct singular varieties associated to a polynomial mapping where such that if G is a local submersion but is not a fibration, then the 2-dimensional homology and intersection homology (with total perversity) of the variety are not trivial. In [2], the authors prove that if there exists a so-called very good projection with respect to the regular value of a polynomial mapping , then this value is an atypical value of G if and only if the Euler characteristic of the fibers is not constant. This paper provides relations of the results obtained in the articles [1] and [2]. Moreover, we provide some examples to illustrate these relations, using the software Maple to complete the calculations of the examples. We provide some discussions on these relations. This paper is an example for graduate students to apply a software that they study in the graduate program in advanced researches.