For algebraically coisotropic X in holomorphic symplectic projective M that is an abelian variety and not uniruled, up to finite etale cover (X,M) is a product with Lagrangian Z in N; when K_X is nef and big, X is Lagrangian in M.
Mattuck, Cycles on abelian varieties, Proc.\ Amer.\ Math.\ Soc.\ 9 (1958), 88--98
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On algebraically coisotropic submanifolds of holomorphic symplectic manifolds
For algebraically coisotropic X in holomorphic symplectic projective M that is an abelian variety and not uniruled, up to finite etale cover (X,M) is a product with Lagrangian Z in N; when K_X is nef and big, X is Lagrangian in M.