<?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>genera(ProjectiveVariety) -- list of the successive linear sectional arithmetic genera</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_genera_lp__Ring_rp.html">next</a> | <a href="_genera_lp__Ideal_rp.html">previous</a> | <a href="_genera_lp__Ring_rp.html">forward</a> | <a href="_genera_lp__Ideal_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>genera(ProjectiveVariety) -- list of the successive linear sectional arithmetic genera</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>genera V</tt></div> </dd></dl> </div> </li> <li><span>Function: <a href="_genera.html" title="list of the successive linear sectional arithmetic genera">genera</a></span></li> <li><div class="single">Inputs:<ul><li><span><tt>V</tt>, <span>a <a href="___Projective__Variety.html">projective variety</a></span></span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>a <a href="___List.html">list</a></span>, of the successive linear sectional arithmetic genera of <tt>V</tt></span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>Computes the list of succesive linear sectional arithmetic genera, where the i-th entry in the list is the arithmetic genus of the i-th succesive generic hyperplane section of <tt>V</tt> (= (-1)^dim-lin-section * (chi(OO_lin-section) - 1)).<p/> A complete intersection of type (2,3) in projective fourspace; its hyperplane section is a canonical curve of genus 4:<table class="examples"><tr><td><pre>i1 : R = ZZ/101[x_0..x_4];</pre> </td></tr> <tr><td><pre>i2 : V = Proj(R/(ideal random(R^1, R^{-2,-3})));</pre> </td></tr> <tr><td><pre>i3 : genera V o3 = {1, 4, 5} o3 : List</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_euler.html" title="Euler characteristic">euler</a> -- Euler characteristic</span></li> <li><span><a href="_genus.html" title="arithmetic genus">genus</a> -- arithmetic genus</span></li> </ul> </div> </div> </body> </html>