On the subvarieties with nonsingular real loci of a real algebraic variety

Abstract

Let $X$ be a smooth projective real algebraic variety. We give new positive and negative results on the problem of approximating a submanifold of the real locus of $X$ by real loci of subvarieties of $X$, as well as on the problem of determining the subgroups of the Chow groups of $X$ generated by subvarieties with nonsingular real loci, or with empty real loci.

Theorems & Definitions (89)

• Theorem 1: Theorem \ref{['Chowth']}
• Theorem 2: Theorem \ref{['Chowth3']}
• Theorem 3: Theorem \ref{['Chowth5']}
• Theorem 4: Theorem \ref{['Chowth2']}
• Theorem 5: Theorem \ref{['Chowth4']}
• Theorem 6: Theorem \ref{['approxth']}
• Theorem 7: Theorem \ref{['thji']}
• Theorem 8: Theorem \ref{['projth']}
• Lemma 1.2
• proof