C = orbitClosure(X,M)
Let $X$ be a generalized flag variety parameterizing flags of linear subspaces of dimensions $\{r_1, ... , r_k\}$ in $\mathbb C^n$ with $1 <= r_1 < \cdots < r_k$. Then a point $p$ of $X$ can be identified with a matrix $M$ of size $r_k \times n$ such that the first $r_i$ rows of $M$ spans a subspace of dimension $r_i$. Given $X$ and such a matrix $M$ representing the point $p$, this method computes the equivariant K-class of the closure of the torus orbit of $p$.
The following example computes the torus orbit closure of a point in the standard Grassmannian $Gr(2,4)$ and in the Lagrangian Grassmannian $SpGr(2,4)$.
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In type "A", the equivariant K-class of the orbit closure of a point coincides with that of its flag matroid.
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In type "D", the orthogonal Grassmannian $SOGr(n,2n)$ has two connected components. To compute the torus orbit closure of a point $p$ it suffices to restrict to either $SOGr(n,n;2n)$ or $SOGr(n-1,n-1;2n)$, depending on which component $p$ is located in; see the last example in Example: generalized flag varieties for more details. Here is an example with $n=4$:
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By default the option RREFMethod is set to false. In this case the method produces the torus orbit closure by only computing the minors of the matrix. If the option RREFMethod is set to true, the method row reduces the matrix instead of computing its minors.
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The object orbitClosure is a method function with options.
The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/GKMVarieties/Documentation_GKMVarieties.m2:1454:0.