On higher Chern classes of vector bundles of conformal blocks

Here we consider higher Chern classes of vector bundles of conformal blocks on ${\stackrel{}{\mathrm{M}}}_{0,n}$, giving explicit formulas for them, and extending various results that hold for first Chern classes to them. We use these classes to form a full dimensional subcone of the Pliant cone on ${\stackrel{}{\mathrm{M}}}_{0,n}$.