  We study the Veronese web equation $u_y u_{tx}+ \lambda u_xu_{ty} -
(\lambda+1)u_tu_{xy} =0$ and using its isospectral Lax pair construct two
infinite series of nonlocal conservation laws. In the infinite differential
coverings associated to these series, we describe the Lie algebras of the
corresponding nonlocal symmetries. Finally, we construct a recursion operator
and explore its action on nonlocal shadows. The operator provides a new shadow
which serves as a master-symmetry.
