  The experimental data on atmospheric and solar neutrinos suggest that there
is near-maximal mixing between \nu_\mu and \nu_\tau but that their masses are
hierarchically separated. In models of Abelian horizontal symmetries, mixing of
O(1) generically implies that the corresponding masses are of the same order of
magnitude. We describe two new mechanisms by which a large hierarchy between
strongly mixed neutrinos can be achieved in this framework. First, a discrete
Abelian symmetry can give the desired result in three ways: mass enhancement,
mixing enhancement and mass suppression. Second, holomorphic zeros can give
mass suppression.

High Energy Physics - Phenomenology