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A Remark on the Topology at Infinity of a Polynomial Mapping F: <span style="font-family:Colonna MT; font-size:20pt;">C</span><sup>n</sup>→<span style="font-family:Colonna MT; font-size:20pt;">C</span><sup>n</sup> via Intersection Homology
UNESP, Universidade Estadual Paulista, “Júlio de Mesquita Filho”, São José do Rio Preto, Brazil
- 1 UNESP, Universidade Estadual Paulista, “Júlio de Mesquita Filho”, São José do Rio Preto, Brazil
Advances in Pure Mathematics·Volume 06 (2016)·Pages 1037–1052·Published 12 December 2016·DOI10.4236/apm.2016.613076
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Abstract
In [1], Guillaume and Anna Valette associate singular varieties V F to a polynomial mapping . In the case , if the set K 0 ( 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 V F 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 0 ( F ) is not empty.
KeywordsPolynomial MappingsIntersection HomologySingularities
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