Smooth torus quotients of Richardson varieties in the Grassmannian

Sarjick Bakshi

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arXiv · 2112.08036

Smooth torus quotients of Richardson varieties in the Grassmannian

Sarjick Bakshi

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Abstract

Let $k$ and $n$ be positive coprime integers with $k<n$. Let $T$ denote the subgroup of diagonal matrices in $SL(n,\mathbb{C})$. We study the GIT quotient of Richardson varieties $X^v_w$ in the Grassmannian $\mathrm{Gr}_{k,n}$ by $T$ with respect to a $T$-linearised line bundle $\cal{L}$ corresponding to the Pl\"{u}cker embedding. We give necessary and sufficient combinatorial conditions for the quotient variety $T \backslash\mkern-6mu\backslash (X_w^v)^{ss}_T({\cal L})$ to be smooth.

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BibTeX RIS

Sarjick Bakshi. 2021-12-15. Smooth torus quotients of Richardson varieties in the Grassmannian. https://arxiv.org/abs/2112.08036

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