  Several lagrangians associated to classical limits of lorenz-violating
fermions in the Standard Model extension (SME) have been shown to yield Finsler
functions when the theory is expressed in Euclidean space. When spin-couplings
are present, the lagrangian can develop singularities that obstruct the
construction of a globally defined Legendre transformation, leading to singular
Finsler spaces. A specific sector of the SME where such problems arise is
studied. It is found that the singular behavior can be eliminated by an
appropriate lifting of the problem to an associated algebraic variety. This
provides a smooth classical model for the singular problem. In Euclidean space,
the procedure involves combining two related singular Finsler functions into a
single smooth function with a semi-positive definite quadratic form defined on
a desingularized variety.
