PieriRootCount -- the number of solutions to a generic Pieri problem

Synopsis

• Usage:

  r = PieriRootCount(m,p,q)

• Inputs:
  • m, an integer, the dimension of the input planes
  • p, an integer, the dimension of the output planes
  • q, an integer, the degree of the solution curves producing p-planes
• Optional inputs:
  • Verbose => ..., default value false, request verbose feedback
• Outputs:
  • r, an integer, the number of curves of the degree $q$ in the Grassmannain $Gr(p,m+p)$ which produce $p$-planes that meet $m\cdot p + q\cdot (m+p)$ generic $m$-planes at given general interpolation points. This is a quantum intersection number

Description

i1 : r := PieriRootCount(3,2,1);

i2 : print r
55