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arXiv · 2307.00203

On $T$-invariant subvarieties of symplectic Grassmannians and representability of rank $2$ symplectic matroids over ${\mathbb C}$

Pedro L. del Angel·E. Javier Elizondo·Cristhian Garay·Felipe Zaldívar
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Abstract

For the symplectic Grassmannian $\text{SpG}(2,2n)$ of $2$-dimensional isotropic subspaces in a $2n$-dimensional vector space over an algebraically closed field of characteristic zero endowed with a symplectic form and with the natural action of an $n$-dimensional torus $T$ on it, we characterize its irreducible $T$-invariant subvarieties. This characterization is in terms of symplectic Coxeter matroids, and we use this result to give a complete characterization of the symplectic matroids of rank $2$ which are representable over $\mathbb{C}$.

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Pedro L. del Angel, E. Javier Elizondo, Cristhian Garay, Felipe Zaldívar. 2023-07-01. On $T$-invariant subvarieties of symplectic Grassmannians and representability of rank $2$ symplectic matroids over ${\mathbb C}$. https://arxiv.org/abs/2307.00203

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