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.

28 pages; v2: improved introduction, Section 4.2 corrected (Lemmas 4.6, 4.7 and 4.9 are new), Section 5 expanded, final version

References in corpus (2)

• On the integral Hodge conjecture for real varieties, I
• On the integral Hodge conjecture for real varieties, II