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schubertCycle -- Schubert Cycles on a Grassmannian in terms of Chern classes of the Tautological bundle.

Synopsis

Description

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
i1 : base(0, Bundle=>(A, 8, a))

o1 = a variety

o1 : an abstract variety of dimension 0
i2 : F=flagBundle ({5,3},A)

o2 = F

o2 : a flag bundle with ranks {5, 3}
where q = 3 and n = 8, we may think of F as the space of projective (q-1)-planes in P(n-1). Fix a complete flag of projective subspaces A0..An-1 in A. The mechanism F(a1..aq) , where 0<= a1 <= .. aq <= n-1 produces the class of the Schubert cycle consisting of those (q-1)-planes meeting Ai in dimensions a1 .. aq.

Caveat

Code only deals with Grassmannians, not with general flag bundles.

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