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<head><title>CoherentSheaf / CoherentSheaf -- quotient of coherent sheaves</title>
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<div><h1>CoherentSheaf / CoherentSheaf -- quotient of coherent sheaves</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>F / G</tt></div>
</dd></dl>
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</li>
<li><span>Operator: <a href="__sl.html" title="a binary operator, usually used for division">/</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>F</tt>, <span>a <a href="___Coherent__Sheaf.html">coherent sheaf</a></span></span></li>
<li><span><tt>G</tt>, <span>a <a href="___Coherent__Sheaf.html">coherent sheaf</a></span>, or <span>an <a href="___Ideal.html">ideal</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Coherent__Sheaf.html">coherent sheaf</a></span>, the quotient sheaf <tt>F/G</tt></span></li>
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<div class="single"><h2>Description</h2>
<div>We compute the cohomology of two sheaves supported on an elliptic curve.<table class="examples"><tr><td><pre>i1 : X = Proj(QQ[x,y,z])
o1 = X
o1 : ProjectiveVariety</pre>
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<tr><td><pre>i2 : I = ideal(y^2*z-x*(x-z)*(x-11*z))
3 2 2 2
o2 = ideal(- x + 12x z + y z - 11x*z )
o2 : Ideal of QQ[x, y, z]</pre>
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<tr><td><pre>i3 : N = (sheaf module I)/(sheaf module I^2)
o3 = subquotient (| -x3+12x2z+y2z-11xz2 |, | x6-24x5z-2x3y2z+166x4z2+24x2y2z2+y4z2-264x3z3-22xy2z3+121x2z4 |)
1
o3 : coherent sheaf on X, subquotient of OO
X</pre>
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<tr><td><pre>i4 : G = OO_X^1/I
o4 = cokernel | -x3+12x2z+y2z-11xz2 |
1
o4 : coherent sheaf on X, quotient of OO
X</pre>
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<tr><td><pre>i5 : HH^1(G)
1
o5 = QQ
o5 : QQ-module, free</pre>
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<tr><td><pre>i6 : HH^1(N)
9
o6 = QQ
o6 : QQ-module, free</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Proj_lp__Ring_rp.html" title="make a projective variety">Proj</a> -- make a projective variety</span></li>
<li><span><a href="___Spec_lp__Ring_rp.html" title="make an affine variety">Spec</a> -- make an affine variety</span></li>
<li><span><a href="_sheaf.html" title="make a coherent sheaf">sheaf</a> -- make a coherent sheaf</span></li>
<li><span><a href="___H__H^__Z__Z_sp__Coherent__Sheaf.html" title="cohomology of a coherent sheaf on a projective variety">HH^ZZ CoherentSheaf</a> -- cohomology of a coherent sheaf on a projective variety</span></li>
<li><span><a href="___O__O_sp_us_sp__Variety.html" title="the structure sheaf">OO</a> -- the structure sheaf</span></li>
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