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<head><title>schubertCycle -- Schubert Cycles on a Grassmannian in terms of Chern classes of the Tautological bundle.</title>
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<div><h1>schubertCycle -- Schubert Cycles on a Grassmannian in terms of Chern classes of the Tautological bundle.</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>c=schubertCycle(F,s)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>F</tt>, <span>an <tt>abstract flag bundle</tt> (missing documentation<!-- tag: FlagBundle -->)</span></span></li>
<li><span><tt>s</tt>, <span>a <a href="../../Macaulay2Doc/html/___Sequence.html">sequence</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>c</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><div>If F is the flag bundle parametrizing subspaces of dimension s and their respective quotient spaces of dimension q of an n-dimensional vector space A, such as</div>
<table class="examples"><tr><td><pre>i1 : base(0, Bundle=>(A, 8, a))
o1 = a variety
o1 : an abstract variety of dimension 0</pre>
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<tr><td><pre>i2 : F=flagBundle ({5,3},A)
o2 = F
o2 : a flag bundle with ranks {5, 3}</pre>
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<div>where q = 3 and n = 8, we may think of F as the space of projective (q-1)-planes in P<sup>(</sup>n-1). Fix a complete flag of projective subspaces A<sub>0</sub>..A<sub>n-1</sub> in A. The mechanism <tt>F<sub>(</sub>a<sub>1</sub>..a<sub>q</sub>) </tt>, where 0<= a<sub>1</sub> <= .. a<sub>q</sub> <= n-1 produces the class of the Schubert cycle consisting of those (q-1)-planes meeting A<sub>i</sub> in dimensions a<sub>1</sub> .. a<sub>q</sub>.</div>
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<div class="single"><h2>Caveat</h2>
<div><div>Code only deals with Grassmannians, not with general flag bundles.</div>
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<div class="waystouse"><h2>Ways to use <tt>schubertCycle</tt> :</h2>
<ul><li><span><tt>schubertCycle(FlagBundle,List)</tt> (missing documentation<!-- tag: (schubertCycle,FlagBundle,List) -->)</span></li>
<li><span><tt>schubertCycle(FlagBundle,Sequence)</tt> (missing documentation<!-- tag: (schubertCycle,FlagBundle,Sequence) -->)</span></li>
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