Seminormalization and continuous rational functions on complex algebraic varieties

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.