A Remark on the Topology at Infinity of a Polynomial Mapping F: Cn→Cn via Intersection Homology

摘要

In [1], Guillaume and Anna Valette associate singular varieties VF to a polynomial mapping . In the case , if the set K0(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 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 K0(F) is not empty.