Stable maps and Chow groups
Daniel Huybrechts, Michael Kemeny

TL;DR
This paper investigates the Bloch-Beilinson conjecture for K3 surfaces, proving it in some cases by using stable maps and elliptic fibrations to analyze automorphisms acting trivially on the transcendental lattice.
Contribution
It demonstrates the conjecture for symplectic involutions on K3 surfaces in one third of cases using stable maps and elliptic surface techniques.
Findings
Proves the conjecture for certain symplectic involutions
Uses stable maps to construct invariant elliptic curves
Identifies conditions under which automorphisms act trivially on CH^2(X)
Abstract
According to the Bloch-Beilinson conjectures, an automorphism of a K3 surface X that acts as the identity on the transcendental lattice should act trivially on CH^2(X). We discuss this conjecture for symplectic involutions and prove it in one third of all cases. The main point is to use special elliptic K3 surfaces and stable maps to produce covering families of elliptic curves on the generic K3 surface that are invariant under the involution.
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
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds
