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schubertCycle -- take a random Schubert cycle

Synopsis

• Usage:
schubertCycle(a,G)
• Inputs:
• a, , a list of integers $a = (a_0,\ldots,a_k)$ with $n-k\geq a_0 \geq \cdots \geq a_k \geq 0$
• G, , which parametrizes the $k$-dimensional subspaces of $\mathbb{P}^n$
• Optional inputs:
• Standard => ..., default value false
• Outputs:
• , the Schubert cycle $\Sigma_a(\mathcal P)\subset\mathbb{G}(k,n)$ associated to a random complete flag $\mathcal P$ of nested projective subspace $\emptyset\subset P_0\subset \cdots \subset P_{n-1} \subset P_{n} = \mathbb{P}^n$ with $dim(P_i)=i$

Description

For the general theory, see e.g. the book 3264 & All That - Intersection Theory in Algebraic Geometry, by D. Eisenbud and J. Harris.

 i1 : G = GG(ZZ/33331,1,5); o1 : ProjectiveVariety, GG(1,5) i2 : S = schubertCycle({2,1},G) o2 = S o2 : ProjectiveVariety, 5-dimensional subvariety of PP^14 (subvariety of codimension 3 in G) i3 : cycleClass S o3 = s 2,1 o3 : ZZ[s , s ] 3,0 2,1