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<head><title>HH^ZZ SheafOfRings -- cohomology of a sheaf of rings on a projective variety</title>
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<div><h1>HH^ZZ SheafOfRings -- cohomology of a sheaf of rings on a projective variety</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>HH^d(R)</tt></div>
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<li><span>Function: <a href="_cohomology.html" title="general cohomology functor">cohomology</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>i</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li>
<li><span><tt>R</tt>, <span>a <a href="___Sheaf__Of__Rings.html">sheaf of rings</a></span>, on a projective variety <tt>X</tt></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Module.html">module</a></span>, the <tt>i</tt>-th cohomology group of <tt>R</tt> as a vector space over the coefficient field of <tt>X</tt></span></li>
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<li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="_cohomology_lp..._cm_sp__Degree_sp_eq_gt_sp..._rp.html">Degree => ...</a>, </span></li>
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<div class="single"><h2>Description</h2>
<div>The command computes the <tt>i</tt>-th cohomology group of <tt>R</tt> as a vector space over the coefficient field of <tt>X</tt>.<p/>
<table class="examples"><tr><td><pre>i1 : Cubic = Proj(QQ[x_0..x_2]/ideal(x_0^3+x_1^3+x_2^3))
o1 = Cubic
o1 : ProjectiveVariety</pre>
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<tr><td><pre>i2 : HH^1(OO_Cubic)
1
o2 = QQ
o2 : QQ-module, free</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_coherent_spsheaves.html" title="">coherent sheaves</a></span></li>
<li><span><a href="___H__H^__Z__Z_sp__Sum__Of__Twists.html" title="coherent sheaf cohomology module">HH^ZZ SumOfTwists</a> -- coherent sheaf cohomology module</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="_hh.html" title="Hodge numbers of a smooth projective variety">hh</a> -- Hodge numbers of a smooth projective variety</span></li>
<li><span><a href="___Coherent__Sheaf.html" title="the class of all coherent sheaves">CoherentSheaf</a> -- the class of all coherent sheaves</span></li>
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