<?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>hirzebruch -- computes the fan of the r-th Hirzebruch surface</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_hypercube.html">next</a> | <a href="_hilbert__Basis.html">previous</a> | <a href="_hypercube.html">forward</a> | <a href="_hilbert__Basis.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>hirzebruch -- computes the fan of the r-th Hirzebruch surface</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> F = hirzebruch r</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>r</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, positive</span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><tt>F</tt>, <span>an object of class <a href="___Fan.html" title="the class of all fans">Fan</a></span></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div><p/> The <tt>r</tt>-th Hirzebruch surface is the <a href="___Fan.html" title="the class of all fans">Fan</a> in <a href="../../Macaulay2Doc/html/___Q__Q.html" title="the class of all rational numbers">QQ</a>^2 generated by the cones <e_1,e_2>, <e_1,-e_2>, <-e_1+r*e_2,-e_2> and <-e_1+r*e_2,e_2>.<table class="examples"><tr><td><pre>i1 : F = hirzebruch 3 o1 = {ambient dimension => 2 } number of generating cones => 4 number of rays => 4 top dimension of the cones => 2 o1 : Fan</pre> </td></tr> <tr><td><pre>i2 : apply(genCones F,rays) o2 = {| 0 -1 |, | 1 0 |, | 1 0 |, | 0 -1 |} | -1 3 | | 0 -1 | | 0 1 | | 1 3 | o2 : List</pre> </td></tr> </table> </div> </div> <div class="waystouse"><h2>Ways to use <tt>hirzebruch</tt> :</h2> <ul><li>hirzebruch(ZZ)</li> </ul> </div> </div> </body> </html>