  We show that a continuous set of degenerate critical soft modes strongly
enhances the first-order character of a fluctuation-induced first-order
transition in the pyrochlore dipolar Heisenberg antiferromagnet. Such a
degeneracy seems essential to explain the strong first-order transition
recently observed in Gd(2)Sn(2)O(7). We present some evidence from Monte-Carlo
simulations and a perturbative renormalization group expansion.
