<?xml version="1.0" encoding="utf-8" ?> <!-- for emacs: -*- coding: utf-8 -*- --> <!-- Apache may like this line in the file .htaccess: AddCharset utf-8 .html --> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" > <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head><title>sheafExt^ZZ(CoherentSheaf,CoherentSheaf) -- sheaf Ext of coherent sheaves</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_sheaf__Hom_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html">next</a> | <a href="_sheaf_lp__Variety_cm__Ring_rp.html">previous</a> | <a href="_sheaf__Hom_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html">forward</a> | <a href="_sheaf_lp__Variety_cm__Ring_rp.html">backward</a> | up | <a href="index.html">top</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> | <a href="http://www.math.uiuc.edu/Macaulay2/">Macaulay2 web site</a></div> </td> </tr> </table> <hr/> <div><h1>sheafExt^ZZ(CoherentSheaf,CoherentSheaf) -- sheaf Ext 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>sheafExt^n(F,G)</tt></div> </dd></dl> </div> </li> <li><span>Scripted functor: <a href="_sheaf__Ext^__Z__Z_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="sheaf Ext of coherent sheaves">sheafExt</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>n</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li> <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></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___Coherent__Sheaf.html">coherent sheaf</a></span>, the n-th sheaf Ext of <tt>F</tt> and <tt>G</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>If <tt>F</tt> or <tt>G</tt> is a sheaf of rings, it is regarded as a sheaf of modules in the evident way.<p/> <tt>F</tt> and <tt>G</tt> must be coherent sheaves on the same projective variety or scheme <tt>X</tt>.<p/> The result is the sheaf associated to the graded module <tt>Ext^n(module M, module N).</tt><table class="examples"><tr><td><pre>i1 : X = Proj(QQ[x,y]) o1 = X o1 : ProjectiveVariety</pre> </td></tr> <tr><td><pre>i2 : sheafExt^1(OO_X^1(2),OO_X(-11)^1) o2 = 0 o2 : coherent sheaf on X</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="___O__O_sp_us_sp__Variety.html" title="the structure sheaf">OO</a> -- the structure sheaf</span></li> <li><span><a href="_sheaf__Hom_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html" title="sheaf Hom">sheafHom</a> -- sheaf Hom</span></li> <li><span><a href="___Hom.html" title="module of homomorphisms">Hom</a> -- module of homomorphisms</span></li> <li><span><a href="___Ext.html" title="compute an Ext module">Ext</a> -- compute an Ext module</span></li> <li><span><a href="___H__H.html" title="general homology and cohomology functor">HH</a> -- general homology and cohomology functor</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> </ul> </div> </div> </body> </html>