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<head><title>CoherentSheaf -- the class of all coherent sheaves</title>
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<div><h1>CoherentSheaf -- the class of all coherent sheaves</h1>
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<div class="waystouse"><h2>Functions and methods returning a coherent sheaf :</h2>
<ul><li><span><a href="_ambient_lp__Coherent__Sheaf_rp.html" title="">ambient(CoherentSheaf)</a></span></li>
<li><span><a href="___Coherent__Sheaf_sp_st_st_sp__Coherent__Sheaf.html" title="tensor produce of coherent sheaves">CoherentSheaf ** CoherentSheaf</a> -- tensor produce of coherent sheaves</span></li>
<li><span><a href="___Coherent__Sheaf_sp_pl_pl_sp__Coherent__Sheaf.html" title="direct sum of coherent sheaves">CoherentSheaf ++ CoherentSheaf</a> -- direct sum of coherent sheaves</span></li>
<li><span><a href="___Coherent__Sheaf_sp_sl_sp__Coherent__Sheaf.html" title="quotient of coherent sheaves">CoherentSheaf / CoherentSheaf</a> -- quotient of coherent sheaves</span></li>
<li><span>CoherentSheaf / Ideal, see <span><a href="___Coherent__Sheaf_sp_sl_sp__Coherent__Sheaf.html" title="quotient of coherent sheaves">CoherentSheaf / CoherentSheaf</a> -- quotient of coherent sheaves</span></span></li>
<li><span><a href="___Coherent__Sheaf_sp^_sp__Z__Z.html" title="direct sum">CoherentSheaf ^ ZZ</a> -- direct sum</span></li>
<li><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></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><a href="_cotangent__Sheaf_lp__Projective__Variety_rp.html" title="cotangent sheaf of a projective variety">cotangentSheaf(ProjectiveVariety)</a> -- cotangent sheaf of a projective variety</span></li>
<li><span><a href="_cotangent__Sheaf_lp__Z__Z_cm__Projective__Variety_rp.html" title="exterior powers of the cotangent sheaf of a projective variety">cotangentSheaf(ZZ,ProjectiveVariety)</a> -- exterior powers of the cotangent sheaf of a projective variety</span></li>
<li><span>cover(CoherentSheaf), see <span><a href="_cover_lp__Module_rp.html" title="get the covering free module">cover(Module)</a> -- get the covering free module</span></span></li>
<li><span><a href="_exterior__Power_lp__Z__Z_cm__Coherent__Sheaf_rp.html" title="exterior power">exteriorPower(ZZ,CoherentSheaf)</a> -- exterior power</span></li>
<li><span>Module ~, see <span><a href="_sheaf_lp__Module_rp.html" title="make a coherent sheaf">sheaf(Module)</a> -- make a coherent sheaf</span></span></li>
<li><span><a href="_sheaf_lp__Module_rp.html" title="make a coherent sheaf">sheaf(Module)</a> -- make a coherent sheaf</span></li>
<li><span><a href="_sheaf_lp__Variety_cm__Module_rp.html" title="make a coherent sheaf">sheaf(Variety,Module)</a> -- make a coherent sheaf</span></li>
<li><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></li>
<li><span>sheafHom, 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>super(CoherentSheaf), see <span><a href="_super.html" title="get the ambient module">super</a> -- get the ambient module</span></span></li>
<li><span><a href="_tangent__Sheaf_lp__Projective__Variety_rp.html" title="tangent sheaf of a projective variety">tangentSheaf(ProjectiveVariety)</a> -- tangent sheaf of a projective variety</span></li>
<li><span>tensor(CoherentSheaf,CoherentSheaf), see <span><a href="_tensor_lp__Module_cm__Module_rp.html" title="tensor product">tensor(Module,Module)</a> -- tensor product</span></span></li>
</ul>
<h2>Methods that use a coherent sheaf :</h2>
<ul><li><span>Ideal * CoherentSheaf, see <span><a href="__st.html" title="a binary operator, usually used for multiplication">*</a> -- a binary operator, usually used for multiplication</span></span></li>
<li><span>annihilator(CoherentSheaf), see <span><a href="_annihilator.html" title="the annihilator ideal">annihilator</a> -- the annihilator ideal</span></span></li>
<li><span>betti(CoherentSheaf), see <span><a href="_betti_lp__Module_rp.html" title="show the degrees of the generators and relations of a module or a coherent sheaf">betti(Module)</a> -- show the degrees of the generators and relations of a module or a coherent sheaf</span></span></li>
<li><span><a href="_codim_lp__Coherent__Sheaf_rp.html" title="codimension of the support of a coherent sheaf on a projective variety">codim(CoherentSheaf)</a> -- codimension of the support of a coherent sheaf on a projective variety</span></li>
<li><span><a href="___Coherent__Sheaf_sp_lp_st_rp.html" title="sum of twists">CoherentSheaf (*)</a> -- sum of twists</span></li>
<li><span><a href="___Coherent__Sheaf_sp^_st_st_sp__Z__Z.html" title="tensor power">CoherentSheaf ^** ZZ</a> -- tensor power</span></li>
<li><span>degrees(CoherentSheaf), see <span><a href="_degrees_lp__Ring_rp.html" title="degrees of generators">degrees(Ring)</a> -- degrees of generators</span></span></li>
<li><span><a href="_dual_lp__Coherent__Sheaf_rp.html" title="dual coherent sheaf">dual(CoherentSheaf)</a> -- dual coherent sheaf</span></li>
<li><span><a href="_euler_lp__Coherent__Sheaf_rp.html" title="Euler characteristic of coherent sheaf">euler(CoherentSheaf)</a> -- Euler characteristic of coherent sheaf</span></li>
<li><span><a href="_eulers_lp__Coherent__Sheaf_rp.html" title="list the sectional Euler characteristics">eulers(CoherentSheaf)</a> -- list the sectional Euler characteristics</span></li>
<li><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></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><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></li>
<li><span><a href="_genera_lp__Coherent__Sheaf_rp.html" title="list of the successive linear sectional arithmetic genera">genera(CoherentSheaf)</a> -- list of the successive linear sectional arithmetic genera</span></li>
<li><span><a href="_genus_lp__Coherent__Sheaf_rp.html" title="arithmetic genus">genus(CoherentSheaf)</a> -- arithmetic genus</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>hilbertFunction(List,CoherentSheaf), see <span><a href="_hilbert__Function.html" title="the Hilbert function">hilbertFunction</a> -- the Hilbert function</span></span></li>
<li><span>hilbertFunction(ZZ,CoherentSheaf), see <span><a href="_hilbert__Function.html" title="the Hilbert function">hilbertFunction</a> -- the Hilbert function</span></span></li>
<li><span><a href="_hilbert__Polynomial_lp__Coherent__Sheaf_rp.html" title="compute the Hilbert polynomial of the coherent sheaf">hilbertPolynomial(CoherentSheaf)</a> -- compute the Hilbert polynomial of the coherent sheaf</span></li>
<li><span><a href="___Hom_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="global Hom">Hom(CoherentSheaf,CoherentSheaf)</a> -- global Hom</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>CoherentSheaf 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>minimalPresentation(CoherentSheaf), see <span><a href="_minimal__Presentation_lp__Module_rp.html" title="minimal presentation of a module">minimalPresentation(Module)</a> -- minimal presentation of a module</span></span></li>
<li><span>prune(CoherentSheaf), see <span><a href="_minimal__Presentation_lp__Module_rp.html" title="minimal presentation of a module">minimalPresentation(Module)</a> -- minimal presentation of a module</span></span></li>
<li><span><a href="_module_lp__Coherent__Sheaf_rp.html" title="get the module defining a coherent sheaf">module(CoherentSheaf)</a> -- get the module defining a coherent sheaf</span></li>
<li><span><a href="_numgens_lp__Coherent__Sheaf_rp.html" title="the number of generators of the underlying module">numgens(CoherentSheaf)</a> -- the number of generators of the underlying module</span></li>
<li><span><a href="_pdim_lp__Coherent__Sheaf_rp.html" title="calculate the projective dimension">pdim(CoherentSheaf)</a> -- calculate the projective dimension</span></li>
<li><span>rank(CoherentSheaf), see <span><a href="_rank.html" title="compute the rank">rank</a> -- compute the rank</span></span></li>
<li><span>ring(CoherentSheaf), 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><a href="_sheaf__Hom_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="sheaf Hom">sheafHom(CoherentSheaf,CoherentSheaf)</a> -- sheaf Hom</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><a href="_variety_lp__Coherent__Sheaf_rp.html" title="">variety(CoherentSheaf)</a></span></li>
</ul>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Coherent__Sheaf.html" title="the class of all coherent sheaves">CoherentSheaf</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> &lt; <a href="___Thing.html" title="the class of all things">Thing</a>.</p>
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