Year: 2025
Type: article
Abstract: The seminormalization of an algebraic variety is the biggest variety which is link to it with a birational, finite and bijective morphism. In this paper, we bring a new understanding to the seminormalization of complex algebraic varieties. We show that it can be obtained by replacing the structural sheaf of the variety by the sheaf of rational functions which extends continuously for the Euclidean topology. We further study this type of functions which can be seen as complex regulous functions, a class of functions recently introduced in real algebraic geometry, or as the algebraic counterpart of c-holomorphic functions.
Source: Annales de l’institut Fourier
DOI: 10.5802/aif.3739
Author: François Bernard
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Centre Henri Lebesgue
OpenAlex ID: W4414390984