In [1], Guillaume and Anna Valette associate singular varieties V<sub>F </sub>to a polynomial mapping . In the case , if the set K<sub>0</sub>(F) of critical values of F is empty, then F is not...In [1], Guillaume and Anna Valette associate singular varieties V<sub>F </sub>to a polynomial mapping . In the case , if the set K<sub>0</sub>(F) of critical values of F is empty, then F is not proper if and only if the 2-dimensional homology or intersection homology (with any perversity) of VF </sub>is not trivial. In [2], the results of [1] are generalized in the case where n≥3, with an additional condition. In this paper, we prove that for a class of non-proper generic dominant polynomial mappings, the results in [1] and [2] hold also for the case that the set K<sub>0</sub>(F) is not empty.展开更多
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 perve...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.展开更多
文摘In [1], Guillaume and Anna Valette associate singular varieties V<sub>F </sub>to a polynomial mapping . In the case , if the set K<sub>0</sub>(F) of critical values of F is empty, then F is not proper if and only if the 2-dimensional homology or intersection homology (with any perversity) of VF </sub>is not trivial. In [2], the results of [1] are generalized in the case where n≥3, with an additional condition. In this paper, we prove that for a class of non-proper generic dominant polynomial mappings, the results in [1] and [2] hold also for the case that the set K<sub>0</sub>(F) is not empty.
文摘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.
