Some notes on the Lê numbers in the family of line singularities

In this paper we introduce the jumps of the Lê numbers of nonisolated singularity f in the family of line deformations. Moreover, we prove the existence of a deformation of a non-degenerate singularity f such that the first Lê number is constant and the zeroth Lê number jumps down to zero. We also give estimations of the Lê numbers when the critical locus is one-dimensional. These give a version of the celebrated theorem of A. G. Kouchnirenko in this case.