One Hat Cyber Team

Edit File: _IHmodule.html

<!DOCTYPE html>
<html lang="en">
  <head>
    <title>IHmodule -- intersection (co)homology module of an irreducible closed subvariety</title>
    <meta content="text/html; charset=utf-8" http-equiv="Content-Type">
    <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css">

o1 = R

o1 : PolynomialRing</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i2 : I=ideal(x^2+y^3)

3    2
o2 = ideal(y  + x )

o2 : Ideal of R</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i3 : IHmodule(I)

o3 = subquotient (| 0  0  |, | dz -x 0  y2 -2ydy-6 0            |)
                  | xy x2 |  | 0  y  dz x  -3ydx   -3xdx-2ydy-8 |

2
o3 : QQ[x..z, dx, dy, dz]-module, subquotient of (QQ[x..z, dx, dy, dz])</code></pre>
            </td>
          </tr>
        </table>
        <div>
          <p>When the given generators of $I$ form a regular sequence, use LocStrategy=>CompleteIntersection for a generally faster algorithm, which implements the determination of the IC module in terms of the fundamental class as described in: D. Barlet and M. Kashiwara, Le réseau $L^2$ d’un système holonome régulier, Invent. Math. 86 (1986), no. 1, 35–62.</p>
        </div>
        <table class="examples">
          <tr>
            <td>
              <pre><code class="language-macaulay2">i4 : R=QQ[x,y]

o4 = R

o4 : PolynomialRing</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i5 : I=ideal(x^2+y^3)

3    2
o5 = ideal(y  + x )

o5 : Ideal of R</code></pre>
            </td>
          </tr>
          <tr>
            <td>
              <pre><code class="language-macaulay2">i6 : IHmodule(I, LocStrategy=>CompleteIntersection)

o6 = subquotient (| x |, | 3xdx+2ydy+6 3y2dx-2xdy y3+x2 |)

1
o6 : QQ[x..y, dx, dy]-module, subquotient of (QQ[x..y, dx, dy])</code></pre>
            </td>
          </tr>
        </table>
      </div>
      <div>
        <h2>Caveat</h2>
        <div>
          <p>Must be a ring of characteristic 0. The ideal $I$ should have only 1 minimal prime.</p>
          <p></p>
        </div>
      </div>
      <div>
        <div class="waystouse">
          <h2>Ways to use <span class="tt">IHmodule</span>:</h2>
          <ul>
            <li><kbd>IHmodule(Ideal)</kbd></li>
          </ul>
        </div>
        <div class="waystouse">
          <h2>For the programmer</h2>
          <p>The object <a title="intersection (co)homology module of an irreducible closed subvariety" href="___I__Hmodule.html">IHmodule</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function__With__Options.html">method function with options</a></span>.</p>
        </div>
        <hr>
        <div class="waystouse">
          <p>The source of this document is in <span class="tt">BernsteinSato/DOC/intersectionCohom.m2:84:0</span>.</p>
        </div>
      </div>
    </div>
  </body>

</html>

Edit File: ___I__Hmodule.html

Edit File: _IHmodule.html