The cyclic polytope C(n,d) is the convex hull of any n points on the
moment curve (t,t2,...,td):t∈R in Rd. For d′>d, we
consider the fiber polytope (in the sense of Billera and Sturmfels) associated
to the natural projection of cyclic polytopes π:C(n,d′)→C(n,d) which
"forgets" the last d′−d coordinates. It is known that this fiber polytope has
face lattice indexed by the coherent polytopal subdivisions of C(n,d) which
are induced by the map π. Our main result characterizes the triples
(n,d,d′) for which the fiber polytope is canonical in either of the following
two senses:
- all polytopal subdivisions induced by π are coherent,
- the structure of the fiber polytope does not depend upon the choice of
points on the moment curve.
We also discuss a new instance with a positive answer to the Generalized
Baues Problem, namely that of a projection π:P→Q where Q has only
regular subdivisions and P has two more vertices than its dimension.Comment: 28 pages with 1 postscript figur