For a licci ideal in a power series ring over a field, it is shown that its conormal module has a free summand precisely when the ideal is a hypersurface section. Using results of B. Ulrich, in the Gorenstein case one can show, up to deformation, that the conormal module is indecomposable.
"Splitting the conormal module for licci ideals." J. Commut. Algebra 14 (1) 55 - 60, Spring 2022. https://doi.org/10.1216/jca.2022.14.55