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arXiv · 2503.16353

Two dimensional versions of the affine Grassmannian and their geometric description

Andrea Maffei·Valerio Melani·Gabriele Vezzosi
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Abstract

For a smooth affine algebraic group $G$ over an algebraically closed field, we consider several two-variables generalizations of the affine Grassmannian $G(\!(t)\!)/G[\![t]\!]$, given by quotients of the double loop group $G(\!(x)\!)(\!(y)\!)$. We prove that they are representable by ind-schemes if $G$ is solvable. Given a smooth surface $X$ and a flag of subschemes of $X$, we provide a geometric interpretation of the two-variables Grassmannians, in terms of bundles and trivialisation data defined on appropriate loci in $X$, which depend on the flag.

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Andrea Maffei, Valerio Melani, Gabriele Vezzosi. 2025-03-20. Two dimensional versions of the affine Grassmannian and their geometric description. https://doi.org/10.1017/fms.2026.10173

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