Daniel Barlet
Univ. Nancy

Abstract: This is a joint work with J. Magnusson. We introduce an interesting class of normal complex spaces having only mild singularities (near to quotient singularities) in which we can generalize the notion of (analytic) fundamental class for complex cycles and also the notion of relative fundamental class for an analytic family of cycles. We also generalize to these spaces the intersection theory for cycles with rational positive coefficients. This also extends to the intersection of analytic families of cycles. We show that almost all the properties of these notions generalize to this context with the exception of the fact that the fundamental classes of the intersection of two cycles whose intersection has the expected co-dimension is not always given by the cup-product of their fundamental classes.
This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.