<?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>sheaf(Variety,Ring) -- make a coherent sheaf of rings</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_sheaf__Ext^__Z__Z_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html">next</a> | <a href="_sheaf_lp__Variety_cm__Module_rp.html">previous</a> | <a href="_sheaf__Ext^__Z__Z_lp__Coherent__Sheaf_cm__Coherent__Sheaf_rp.html">forward</a> | <a href="_sheaf_lp__Variety_cm__Module_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>sheaf(Variety,Ring) -- make a coherent sheaf of rings</h1> <div class="single"><h2>Synopsis</h2> <ul><li><span>Function: <a href="_sheaf.html" title="make a coherent sheaf">sheaf</a></span></li> </ul> </div> <div class="single"><h2>Description</h2> <div><tt>sheaf(X,R)</tt> -- produce the coherent sheaf on the variety <tt>X</tt> corresponding to the ring <tt>R</tt>. The variety <tt>X</tt> must be <tt>Spec R</tt> or <tt>Proj R</tt>.<table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z] o1 = R o1 : PolynomialRing</pre> </td></tr> <tr><td><pre>i2 : X = Proj R o2 = X o2 : ProjectiveVariety</pre> </td></tr> <tr><td><pre>i3 : Y = Spec R o3 = Y o3 : AffineVariety</pre> </td></tr> <tr><td><pre>i4 : sheaf(X,R) o4 = OO X o4 : SheafOfRings</pre> </td></tr> <tr><td><pre>i5 : sheaf(Y,R) o5 = OO Y o5 : SheafOfRings</pre> </td></tr> </table> </div> </div> </div> </body> </html>