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Weak and semi normalization in real algebraic geometry (1706.04467v3)
Published 14 Jun 2017 in math.AG and math.AC
Abstract: We define the weak-normalization and the seminormalization of a real algebraic variety relative to its central locus. The study is related to the properties of the rings of continuous rational functions and hereditarily rational functions on real algebraic varieties. We provide in particular several characterizations (algebraic or geometric) of these varieties, and provide a full description of centrally seminormal curves.