Correspondences acting on constant cycle curves on K3 surfaces

Constant cycle curves on a K3 surface X over C are curves whose points all define the same class in the Chow group. In this paper we study correspondences Z⊆X×X over C acting on the group ccc(X) of cycles generated by irreducible constant cycle curves. We construct for any n≥2 and any very ample line bundle L a locus Zn(L)⊆X×X which is expected to have dimension 2 and which yields a correspondence that acts on ccc(X), when it has dimension 2. We provide examples of Zn(L) for low n and exhibit one correspondence different from Zn(L) acting on ccc(X).