Mathematische Zeitschrift

, Volume 292, Issue 1–2, pp 317–341 | Cite as

On nearly smooth complex spaces

  • Daniel Barlet
  • Jón MagnússonEmail author


We introduce a class of normal complex spaces having only mild singularities (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.


Quotient singularity The sheaf \(\omega _{X}^{\bullet }\) Fundamental class of cycles Analytic family of cycles Geometric intersection theory 

Mathematics Subject classifications

32 C 20 32 C 25 32 C 36 



The authors would like to thank the referee for comments that lead to improvements of the paper.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut Elie Cartan, Géomètrie, Université de Lorraine, CNRS UMR 7502 and Institut Universitaire de FranceNancyFrance
  2. 2.Department of Mathematics, School of Engineering and Physical SciencesUniversity of IcelandReykjavíkIceland

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