Universally equidimensional morphisms and weakly-1-rational or weakly-2-rational singularities
Mohamed Kaddar
Journal of Singularities
volume 28 (2025), 1-52
Received: 10 July 2025. In revised form: 10 February 2026
Abstract:
This article aims to study the behavior of certain types of singularities in a universally equidimensional morphism (i.e., open with constant pure-dimensional fibers). These singularities are those of reduced complex spaces of pure dimension m for which the sheaf {\mathcal L}^m_Z (whose sections are meromorphic forms that extend analytically over any desingularization of Z) has depth at least two and are called weakly-1-rational and denoted {\mathfrak{WR}}^1; for spaces whose singular locus is of codimension at least two, they are called weakly-2-rational and denoted {\mathfrak{WR}}^2. Our study focuses on the possibility of transferring this type of singularities from the total space to the base, from the base and the fibers to the total space, and from the latter to the fibers.
2010 Mathematical Subject Classification:
14B05, 14B15, 32S20
Key words and phrases:
Analytic spaces, Integration, cohomology, dualizing sheaves
Author(s) information:
Mohamed Kaddar
email: mohamed.kaddar@univ-lorraine.fr