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<?xml version="1.0" encoding="UTF-8" ?>DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd " >html xmlns="http://www.w3.org/1999/xhtml " xml:lang="en" >head >script type="text/javascript" "https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML " >script >title >GAP (GradedModules) - Chapter 2: Ring Maps</title >meta http-equiv="content-type" content="text/html; charset=UTF-8" />meta name="generator" content="GAPDoc2HTML" />link rel="stylesheet" type="text/css" href="manual.css" />script src="manual.js" type="text/javascript" ></script >script type="text/javascript" >overwriteStyle();</script >head >body class="chap2" onload="jscontent()" >div class="chlinktop" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0_mj.html" >Top</a> <a href="chap1_mj.html" >1</a> <a href="chap2_mj.html" >2</a> <a href="chap3_mj.html" >3</a> <a href="chap4_mj.html" >4</a> <a href="chap5_mj.html" >5</a> <a href="chapBib_mj.html" >Bib</a> <a href="chapInd_mj.html" >Ind</a> </div >div class="chlinkprevnexttop" > <a href="chap0_mj.html" >[Top of Book]</a> <a href="chap0_mj.html#contents" >[Contents]</a> <a href="chap1_mj.html" >[Previous Chapter]</a> <a href="chap3_mj.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap2.html" >[MathJax off]</a></p>"X7B222197819984A6" name="X7B222197819984A6" ></a></p>div class="ChapSects" ><a href="chap2_mj.html#X7B222197819984A6" >2 <span class="Heading" >Ring Maps</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X7EBF1DD67BD0758F" >2.1 <span class="Heading" >Ring Maps: Attributes</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X87C00FFB79FA93A8" >2.1-1 KernelSubobject</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X7C7401BA7E2221CB" >2.2 <span class="Heading" >Ring Maps: Operations and Functions</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7B7DDDA17837AEF5" >2.2-1 SegreMap</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X78E0B36179C5646C" >2.2-2 PlueckerMap</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X816B9AB287EEF9A5" >2.2-3 VeroneseMap</a></span >div ></div >div >span class="Heading" >Ring Maps</span ></h3>"X7EBF1DD67BD0758F" name="X7EBF1DD67BD0758F" ></a></p>span class="Heading" >Ring Maps: Attributes</span ></h4>"X87C00FFB79FA93A8" name="X87C00FFB79FA93A8" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ KernelSubobject</code >( <var class="Arg" >phi</var > )</td ><td class="tdright" >( method )</td ></tr ></table ></div >strong class="pkg" >homalg</strong > submodule</p>map <var class="Arg" >phi</var >.</p>"X7C7401BA7E2221CB" name="X7C7401BA7E2221CB" ></a></p>span class="Heading" >Ring Maps: Operations and Functions</span ></h4>"X7B7DDDA17837AEF5" name="X7B7DDDA17837AEF5" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ SegreMap</code >( <var class="Arg" >R</var >, <var class="Arg" >s</var > )</td ><td class="tdright" >( method )</td tr ></table ></div >strong class="pkg" >homalg</strong > ring map </p>map corresponding to the Segre embedding of <span class="SimpleMath" >\(MultiProj(\textit{R})\)</span > into the projective space according to <span class="SimpleMath" >\(P(W_1)\times P(W_2) \to P(W_1\otimes W_2)\)</span >.</p>"X78E0B36179C5646C" name="X78E0B36179C5646C" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ PlueckerMap</code >( <var class="Arg" >l</var >, <var class="Arg" >n</var >, <var class="Arg" >A</var >, <var class="Arg" >s</var > )</td ><td class="tdright" >( method )</td ></tr ></table ></div >strong class="pkg" >homalg</strong > ring map </p>map corresponding to the Plücker embedding of the Grassmannian <span class="SimpleMath" >\(G_l(P^{\textit{n}}(\textit{A}))=G_l(P(W))\)</span > into the projective space <span class="SimpleMath" >\(P(\bigwedge^l W)\)</span >, where <span class="SimpleMath" >\(W=V^*\)</span > is the <span class="SimpleMath" >\(\textit{A}\)</span >-dual of the free module <span class="SimpleMath" >\(V=A^{\textit{n}+1}\)</span > of rank <span class="SimpleMath" >\(\textit{n}+1\)</span >.</p>"X816B9AB287EEF9A5" name="X816B9AB287EEF9A5" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ VeroneseMap</code >( <var class="Arg" >n</var >, <var class="Arg" >d</var >, <var class="Arg" >A</var >, <var class="Arg" >s</var > )</td ><td class="tdright" >( method )</td ></tr ></table ></div >strong class="pkg" >homalg</strong > ring map </p>map corresponding to the Veronese embedding of the projective space <span class="SimpleMath" >\(P^{\textit{n}}(\textit{A})=P(W)\)</span > into the projective space <span class="SimpleMath" >\(P(S^d W)\)</span >, where <span class="SimpleMath" >\(W=V^*\)</span > is the <span class="SimpleMath" >\(\textit{A}\)</span >-dual of the free module <span class="SimpleMath" >\(V=A^{\textit{n}+1}\)</span > of rank <span class="SimpleMath" >\(\textit{n}+1\)</span >.</p>div class="chlinkprevnextbot" > <a href="chap0_mj.html" >[Top of Book]</a> <a href="chap0_mj.html#contents" >[Contents]</a> <a href="chap1_mj.html" >[Previous Chapter]</a> <a href="chap3_mj.html" >[Next Chapter]</a> </div >div class="chlinkbot" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0_mj.html" >Top</a> <a href="chap1_mj.html" >1</a> <a href="chap2_mj.html" >2</a> <a href="chap3_mj.html" >3</a> <a href="chap4_mj.html" >4</a> <a href="chap5_mj.html" >5</a> <a 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