Other separating morphisms

Determine which covering-degree vectors arise from separating morphisms of the normalization of an irreducible component of a finite free curve C_w to \mathbf P^1, and characterize the resulting separating semigroup directly in terms of the input velocities.

Background

For the distinguished projection from the normalized finite free curve to the real projective parameter line, the paper computes the covering degrees from ordered collision multiplicities via block and global reversals. These degrees provide one degree vector in the separating semigroup associated with the normalized component.

The authors leave unresolved the broader collection of separating morphisms and whether their possible degree vectors can be described using the input velocity data. This problem concerns the geometry beyond the particular projection used throughout the paper.