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Constant cycle curves on a K3 surface $X$ over $\mathbb{C}$ have beenintroduced by Huybrechts (2014) as curves whose points all define the sameclass in the Chow group. In this paper we study correspondences $Z \subseteqX\times X$ over $\mathbb{C}$ acting on the group $\mbox{ccc}(X)$ of cyclesgenerated by irreducible constant cycle curves. We construct for any $n\geq 2$and any very ample line bundle $L$ a locus $Z_n(L)\subseteq X\times X$ ofexpected dimension $2$, which yields a correspondence that acts on$\mbox{ccc}(X)$, when it has the expected dimension. We provide examples of$Z_n(L)$ for low $n$ and exhibit one correspondence different from $Z_n(L)$acting on $\mbox{ccc}(X)$.

Correspondences acting on constant cycle curves on K3 surfaces