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

Benoist, Olivier

doi:10.2140/gt.2024.28.1693

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

Olivier Benoist

Geometry & Topology 28 (2024) 1693–1725

DOI: 10.2140/gt.2024.28.1693

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.

Keywords

real algebraic geometry, algebraic cycles, linkage, cobordism

Mathematical Subject Classification

Primary: 13C40, 14C15, 14P05, 55N22

References

Publication

Received: 30 March 2021

Revised: 26 September 2022

Accepted: 22 October 2022

Published: 18 July 2024

Proposed: Haynes R Miller

Seconded: Dan Abramovich, Mark Gross

Authors

Olivier Benoist
Département de mathématiques et applications École normale supérieure CNRS Paris France

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Volume 28, issue 4 (2024)