Title: On the nearly smooth complex spaces,
Abstract: We introduce a class of normal complex spaces having only mild sin-gularities
(close to quotient singularities) for which we generalize the notion of a
(analytic) fundamental class for an analytic cycle and also the notion of a
relative fundamental class for an analytic family of cycles. We also generalize
to these spaces the geometric intersection theory for analytic cycles with
rational positive coefficients and show that it behaves well with respect to
analytic families of cycles. We prove that this intersection theory has most of
the usual properties of the standard geometric intersection theory on complex
manifolds, but with the exception that the intersection cycle of two cycles
with positive integral coefficients that intersect properly may have rational
coefficients. AMS classification. 32 C 20-32 C 25-32 C 36.