# Fano(ZZ,Ideal,Ring) -- Fano scheme

## Synopsis

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

## Description

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.