Correspondences acting on constant cycle curves on K3 surfaces

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