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<head><title>Fano(ZZ,Ideal) -- Fano scheme</title>
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<div><h1>Fano(ZZ,Ideal) -- Fano scheme</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>Fano(k,I)</tt></div>
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<li><span>Function: <a href="___Fano.html" title="Fano scheme">Fano</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>k</tt>, <span>an <a href="___Z__Z.html">integer</a></span>, a positive integer less than <tt>r</tt></span></li>
<li><span><tt>I</tt>, <span>an <a href="___Ideal.html">ideal</a></span>, an ideal representing a variety in in projective <tt>r</tt>-space</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>an <a href="___Ideal.html">ideal</a></span>, the ideal of a Fano scheme in the Grassmannian</span></li>
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<div class="single"><h2>Description</h2>
<div>Given an ideal <tt>I</tt> representing a projective variety <tt>X</tt> in <tt>P^r</tt>, a positive integer k<r, and optionally a ring <tt>GR</tt> with (exactly) <tt>r+1</tt> choose <tt>k+1</tt> variables, representing the ambient space of the Grassmannian of k-planes in <tt>P^r</tt>, this routine returns the ideal in <tt>GR</tt> of the Fano scheme that parametrizes the k-planes lying on <tt>X</tt>. If the optional third argument is not present, the routine fabricates its own ring, and returns an ideal in it.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Fano_lp__Z__Z_cm__Ideal_cm__Ring_rp.html" title="Fano scheme">Fano(ZZ,Ideal,Ring)</a> -- Fano scheme</span></li>
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