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<head><title>SheafOfRings -- the class of sheaves of rings</title>
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<div><h1>SheafOfRings -- the class of sheaves of rings</h1>
<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : X = Proj(QQ[x..z])
o1 = X
o1 : ProjectiveVariety</pre>
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<tr><td><pre>i2 : OO_X
o2 = OO
X
o2 : SheafOfRings</pre>
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<tr><td><pre>i3 : OO_X^6
6
o3 = OO
X
o3 : coherent sheaf on X, free</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Variety.html" title="the class of all algebraic varieties">Variety</a> -- the class of all algebraic varieties</span></li>
<li><span><a href="___O__O_sp_us_sp__Variety.html" title="the structure sheaf">OO</a> -- the structure sheaf</span></li>
</ul>
</div>
<div class="waystouse"><h2>Functions and methods returning a sheaf of rings :</h2>
<ul><li><span>Ring ~, see <span><a href="_sheaf_lp__Ring_rp.html" title="make a coherent sheaf of rings">sheaf(Ring)</a> -- make a coherent sheaf of rings</span></span></li>
<li><span><a href="_sheaf_lp__Ring_rp.html" title="make a coherent sheaf of rings">sheaf(Ring)</a> -- make a coherent sheaf of rings</span></li>
<li><span><a href="_sheaf_lp__Variety_cm__Ring_rp.html" title="make a coherent sheaf of rings">sheaf(Variety,Ring)</a> -- make a coherent sheaf of rings</span></li>
</ul>
<h2>Methods that use a sheaf of rings :</h2>
<ul><li><span>SheafOfRings (*), see <span><a href="___Coherent__Sheaf_sp_lp_st_rp.html" title="sum of twists">CoherentSheaf (*)</a> -- sum of twists</span></span></li>
<li><span>SheafOfRings ^ ZZ, see <span><a href="___Coherent__Sheaf_sp^_sp__Z__Z.html" title="direct sum">CoherentSheaf ^ ZZ</a> -- direct sum</span></span></li>
<li><span>SheafOfRings ZZ, see <span><a href="___Coherent__Sheaf_sp__Z__Z.html" title="canonical twist of a coherent sheaf">CoherentSheaf ZZ</a> -- canonical twist of a coherent sheaf</span></span></li>
<li><span>Ext^ZZ(CoherentSheaf,SheafOfRings), see <span><a href="___Ext^__Z__Z_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="global Ext">Ext^ZZ(CoherentSheaf,CoherentSheaf)</a> -- global Ext</span></span></li>
<li><span>Ext^ZZ(SheafOfRings,CoherentSheaf), see <span><a href="___Ext^__Z__Z_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="global Ext">Ext^ZZ(CoherentSheaf,CoherentSheaf)</a> -- global Ext</span></span></li>
<li><span>Ext^ZZ(SheafOfRings,SheafOfRings), see <span><a href="___Ext^__Z__Z_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="global Ext">Ext^ZZ(CoherentSheaf,CoherentSheaf)</a> -- global Ext</span></span></li>
<li><span>Ext^ZZ(SheafOfRings,SumOfTwists), see <span><a href="___Ext^__Z__Z_lp__Coherent__Sheaf_cm__Sum__Of__Twists_rp.html" title="global Ext">Ext^ZZ(CoherentSheaf,SumOfTwists)</a> -- global Ext</span></span></li>
<li><span><a href="___H__H^__Z__Z_sp__Sheaf__Of__Rings.html" title="cohomology of a sheaf of rings on a projective variety">HH^ZZ SheafOfRings</a> -- cohomology of a sheaf of rings on a projective variety</span></li>
<li><span>Hom(CoherentSheaf,SheafOfRings), see <span><a href="___Hom_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="global Hom">Hom(CoherentSheaf,CoherentSheaf)</a> -- global Hom</span></span></li>
<li><span>Hom(SheafOfRings,CoherentSheaf), see <span><a href="___Hom_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="global Hom">Hom(CoherentSheaf,CoherentSheaf)</a> -- global Hom</span></span></li>
<li><span>Hom(SheafOfRings,SheafOfRings), see <span><a href="___Hom_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="global Hom">Hom(CoherentSheaf,CoherentSheaf)</a> -- global Hom</span></span></li>
<li><span>SheafOfRings LowerBound, see <span><a href="___Lower__Bound.html" title="the class of lower bound objects">LowerBound</a> -- the class of lower bound objects</span></span></li>
<li><span><a href="_module_lp__Sheaf__Of__Rings_rp.html" title="make or get a module">module(SheafOfRings)</a> -- make or get a module</span></li>
<li><span>ring(SheafOfRings), see <span><a href="_ring.html" title="get the associated ring of an object">ring</a> -- get the associated ring of an object</span></span></li>
<li><span>sheafExt^ZZ(CoherentSheaf,SheafOfRings), see <span><a href="_sheaf__Ext^__Z__Z_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="sheaf Ext of coherent sheaves">sheafExt^ZZ(CoherentSheaf,CoherentSheaf)</a> -- sheaf Ext of coherent sheaves</span></span></li>
<li><span>sheafExt^ZZ(SheafOfRings,CoherentSheaf), see <span><a href="_sheaf__Ext^__Z__Z_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="sheaf Ext of coherent sheaves">sheafExt^ZZ(CoherentSheaf,CoherentSheaf)</a> -- sheaf Ext of coherent sheaves</span></span></li>
<li><span>sheafExt^ZZ(SheafOfRings,SheafOfRings), see <span><a href="_sheaf__Ext^__Z__Z_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="sheaf Ext of coherent sheaves">sheafExt^ZZ(CoherentSheaf,CoherentSheaf)</a> -- sheaf Ext of coherent sheaves</span></span></li>
<li><span>sheafHom(CoherentSheaf,SheafOfRings), see <span><a href="_sheaf__Hom_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="sheaf Hom">sheafHom(CoherentSheaf,CoherentSheaf)</a> -- sheaf Hom</span></span></li>
<li><span>sheafHom(SheafOfRings,CoherentSheaf), see <span><a href="_sheaf__Hom_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="sheaf Hom">sheafHom(CoherentSheaf,CoherentSheaf)</a> -- sheaf Hom</span></span></li>
<li><span>sheafHom(SheafOfRings,SheafOfRings), see <span><a href="_sheaf__Hom_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="sheaf Hom">sheafHom(CoherentSheaf,CoherentSheaf)</a> -- sheaf Hom</span></span></li>
<li><span><a href="___Sheaf__Of__Rings_sp^_sp__List.html" title="make a graded free coherent sheaf">SheafOfRings ^ List</a> -- make a graded free coherent sheaf</span></li>
<li><span><a href="_variety_lp__Sheaf__Of__Rings_rp.html" title="get the variety">variety(SheafOfRings)</a> -- get the variety</span></li>
</ul>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Sheaf__Of__Rings.html" title="the class of sheaves of rings">SheafOfRings</a> is <span>a <a href="___Type.html">type</a></span>, with ancestor classes <a href="___Hash__Table.html" title="the class of all hash tables">HashTable</a> < <a href="___Thing.html" title="the class of all things">Thing</a>.</p>
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