Fano -- compute the ideal of a Fano scheme in the Grassmannian

Fano scheme

• Usage:

  Fano(k,I)

• Inputs:
  • k, a positive integer less than r
  • I, an ideal representing a variety in projective r-space
• Outputs:
  • the ideal of a Fano scheme in the Grassmannian

Given an ideal I representing a projective variety X in P^r, a positive integer k<r, and optionally a ring GR with (exactly) r+1 choose k+1 variables, representing the ambient space of the Grassmannian of k-planes in P^r, this routine returns the ideal in GR of the Fano scheme that parametrizes the k-planes lying on X. If the optional third argument is not present, the routine fabricates its own ring, and returns an ideal in it.

Synopsis

• Usage:

  Fano(k,I,GR)

• Inputs:
  • k, a positive integer less than r
  • I, an ideal representing a variety in projective r-space
  • GR,
• Outputs:
  • the ideal of a Fano scheme in the Grassmannian

Given an ideal I representing a projective variety X in P^r, a positive integer k<r, and optionally a ring GR with (exactly) r+1 choose k+1 variables, representing the ambient space of the Grassmannian of k-planes in P^r, this routine returns the ideal in GR of the Fano scheme that parametrizes the k-planes lying on X. If the optional third argument is not present, the routine fabricates its own ring, and returns an ideal in it.