Initial degenerations of spinor varieties

TL;DR

This paper studies the initial degenerations of spinor varieties, showing they are smooth and irreducible for small dimensions, and connects these degenerations to log canonical models of Chow quotients.

Contribution

It constructs explicit embeddings of initial degenerations into inverse limits of strata related to even Δ-matroids, providing new geometric insights.

Findings

Initial degenerations are smooth and irreducible for n ≤ 5.

Constructs closed immersions into inverse limits of strata.

Identifies the log canonical model of the Chow quotient of S_5.

Abstract

We construct closed immersions from initial degenerations of the spinor variety $\mathbb{S}_n$ to inverse limits of strata associated to even $\Delta$-matroids. As an application, we prove that these initial degenerations are smooth and irreducible for $n\leq 5$ and identify the log canonical model of the Chow quotient of $\mathbb{S}_5$ by the action of the diagonal torus of $\operatorname{GL}(5)$.