Seminormalization and regulous functions on complex affine varieties

2021/09/14 by Bernard, François
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.06542

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.

Related

• Weak and semi normalization in real algebraic geometry
• A notion of seminormalization for real algebraic varieties
• Extension of k-regulous functions from varieties of arbitrary dimension
• Semi-algebraic geometry with rational continuous functions
• Extensions of k-regulous functions from two-dimensional varieties