  Non-centrosymmetric superconductors have recently attracted much attention,
since the lack of inversion symmetry mixes spin singlet and triplet pairing
states, which may allow the realization of topological superconductivity. In
this work, we study the electronic properties of the family of inversion-broken
CeTX$_3$ heavy-fermion superconductors, finding topological nodal lines as well
as Dirac and Weyl points, which are renormalized closer to the Fermi energy by
correlations. We find that the Weyl nodal lines have a substantial effect on
the Fermi surface spin structure of the normal state, and lead to line nodes in
the superconducting phase.
