TITLE:
A Remark on Polynomial Mappings from Cn to Cn-1 and an Application of the Software Maple in Research
AUTHORS:
Thi Bich Thuy Nguyen
KEYWORDS:
Singularities, Intersection Homology, Polynomial Mappings, Bifurcation
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.15,
September
29,
2016
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.