document {
     Key => Fano, 
     Headline => "Fano scheme"
     }

document {
	Key => (Fano,ZZ,Ideal),
	Headline => "Fano scheme",
	Usage => "Fano(k,I)",
	Inputs => {
		"k" => {"a positive integer less than ", TT "r"},
		"I" => {"an ideal representing a variety in projective ", TT "r", "-space"}, 
		},
	Outputs => {"the ideal of a Fano scheme in the Grassmannian"},
	  "Given an ideal ", TT "I", " representing a projective variety ", TT "X", "
     in ", TT "P^r", ", a positive integer k<r, and optionally a 
     ring ", TT "GR", " with (exactly) ", TT "r+1", " choose ", TT "k+1", " variables, 
     representing the ambient space of the Grassmannian of 
     k-planes in ", TT "P^r", ", this routine returns the ideal in
     ", TT "GR", " of the Fano scheme that parametrizes the k-planes 
     lying on ", TT "X", ".  If the optional third argument is not 
     present, the routine fabricates its own ring, 
     and returns an ideal in it.",
	SeeAlso => (Fano,ZZ,Ideal,Ring)
	}

document {
	Key => (Fano,ZZ,Ideal,Ring),
	Headline => "Fano scheme",
	Usage => "Fano(k,I,GR)",
	Inputs => {
		"k" => {"a positive integer less than ", TT "r"},
		"I" => {"an ideal representing a variety in projective ", TT "r", "-space"},
		"GR" => {} 
		},
	Outputs => {"the ideal of a Fano scheme in the Grassmannian"},
	  "Given an ideal ", TT "I", " representing a projective variety ", TT "X", "
     in ", TT "P^r", ", a positive integer k<r, and optionally a 
     ring ", TT "GR", " with (exactly) ", TT "r+1", " choose ", TT "k+1", " variables, 
     representing the ambient space of the Grassmannian of 
     k-planes in ", TT "P^r", ", this routine returns the ideal in
     ", TT "GR", " of the Fano scheme that parametrizes the k-planes 
     lying on ", TT "X", ".  If the optional third argument is not 
     present, the routine fabricates its own ring, 
     and returns an ideal in it.",
	SeeAlso => (Fano,ZZ,Ideal)
	}
