Curve Classes on Rationally Connected Varieties
Hong R. Zong
TL;DR
This paper proves that on rationally connected varieties, every curve can be algebraically expressed as a sum of rational curves, enhancing understanding of their geometric structure.
Contribution
It establishes that all curves on rationally connected varieties are algebraically equivalent to sums of rational curves, providing a new perspective on their geometry.
Findings
Every curve is algebraically equivalent to a sum of rational curves
Advances understanding of the structure of rationally connected varieties
Provides a foundation for further geometric and algebraic studies
Abstract
We prove that every curve on a rationally connected variety is algebraically equivalent to a (non-effective) integral sum of rational curves.
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
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Advanced Numerical Analysis Techniques