I'm looking for Web-accessible references that survey the connnections among the following constructs:
- discriminant varieties
- Vandermonde matrix/determinant/polynomial
- moment curves for the n-simplices, the cyclic polytopes
- Legendre-Fenchel transform/compositional inversion
- Lagrangian-Hamiltonian duality,
something along the lines of "How tangents solve algebraic equations, or a remarkable geometry of discriminant varieties" by Katz and a little more pedestrian than say "Simple Lie algebras and Legendre varieties" by Mukai.
(One example of info that can be easily decoded from relations among 1,2,4, and 5 is the convergence limit for the Taylor series expansions of the solutions about the origin of the family of equations
$$y=x+t \cdot x^n,$$
whose coefficients are the Fuss-Catalan numbers.)
