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# schubertCycle -- take a random Schubert cycle

- Usage:
    `schubertCycle(a,G)`
- Inputs:
  - a, a visible list, a list of integers $a = (a_0,\ldots,a_k)$ with $n-k\geq a_0 \geq \cdots \geq a_k \geq 0$
  - G, a Grassmannian variety, which parametrizes the $k$-dimensional subspaces of $\mathbb{P}^n$
- Optional inputs:
  - Standard => ..., default value false
- Outputs:
  - an embedded projective variety, 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

## See also

- cycleClass -- determine the expression of the class of a cycle as a linear combination of Schubert classes

## Ways to use schubertCycle:

- `schubertCycle(VisibleList,GrassmannianVariety)`

## For the programmer

The object schubertCycle is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/MultiprojectiveVarieties.m2:4031:0.