Fano(ZZ,Ideal,Ring) -- Fano scheme
Synopsis
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Function: Fano
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- Usage:
Fano(k,I,GR)
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Inputs:
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k, an integer, a positive integer less than r
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I, an ideal, an ideal representing a variety in projective r-space
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GR, a ring,
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Outputs:
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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.