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<head><title>genera(CoherentSheaf) -- list of the successive linear sectional arithmetic genera</title>
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<div><h1>genera(CoherentSheaf) -- 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 M</tt></div>
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<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>M</tt>, <span>a <a href="___Coherent__Sheaf.html">coherent sheaf</a></span></span></li>
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<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 the succesive generic hyperplane restrictions of <tt>M</tt></span></li>
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<div class="single"><h2>Description</h2>
<div>Computes the list of succesive generic linear sectional arithmetic genera, where the i-th entry in the list is (-1)^dim-support -i * (chi(M ** OO_lin-section) - 1)).<table class="examples"><tr><td><pre>i1 : V = Proj(ZZ/101[x_0..x_2]);</pre>
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<tr><td><pre>i2 : M = sheaf(image matrix {{x_0^3+x_1^3+x_2^3}})
o2 = image | x_0^3+x_1^3+x_2^3 |
1
o2 : coherent sheaf on V, subsheaf of OO
V</pre>
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<tr><td><pre>i3 : genera M
o3 = {0, 3, 0}
o3 : List</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_euler.html" title="Euler characteristic">euler</a> -- Euler characteristic</span></li>
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