The M5-brane on K3 x T²

We discuss the low energy effective theory of an M5-brane wrapped on a smooth holomorphic four-cycle of K3 x T^2, including the special case of T^6. In particular we give the lowest order equations of motion and resolve a puzzle concerning the counting of massless modes that was reported in hep-th/9906094. In order to find agreement with black hole entropy and anomaly inflow arguments we propose that some of the moduli become massive.