Real affine varieties of nonnegative curvature
Xiaoyang Chen

TL;DR
This paper proves that smooth real affine varieties with compact real points and a conjugation-invariant nonnegative curvature metric are diffeomorphic to the normal bundle of their real points, linking curvature conditions to topological structure.
Contribution
It establishes a new topological classification of real affine varieties under nonnegative curvature conditions with conjugation symmetry.
Findings
Real affine varieties with the specified conditions are diffeomorphic to the normal bundle of their real points.
The result connects geometric curvature properties with the topological structure of algebraic varieties.
Provides a criterion for the topological type of real affine varieties based on curvature and symmetry.
Abstract
Let be a smooth real affine variety with compact real points . We show that is diffeomorphic to the normal bundle of provided that admits a complete Riemannian metric of nonnegative sectional curvature which is also invariant under the conjugation.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology
