Seminormalization and regulous functions on complex affine varieties

TL;DR

This paper explores seminormalization of affine complex varieties and characterizes polynomials on seminormalizations as continuous rational functions, linking complex regulous functions with algebraic and topological properties.

Contribution

It introduces a new perspective on complex regulous functions as polynomials on seminormalizations, connecting algebraic geometry with topological continuity.

Findings

Polynomials on seminormalizations correspond to Euclidean continuous rational functions.

Complex regulous functions are characterized as algebraic counterparts of c-holomorphic functions.

The study bridges algebraic, topological, and complex analytic perspectives in affine varieties.

Abstract

We study seminormalization of affine complex varieties. We show that polynomials on the seminormalization correspond to the rational functions which are continuous 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.