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arXiv · 2603.05808

Compactifications of spaces of symmetric matrices and pointed Kontsevich spaces of isotropic Grassmannians

Hanlong Fang·Alex Massarenti·Xian Wu
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Abstract

We study two closely related families of varieties arising from genus $0$ stable maps to the Lagrangian Grassmannian $\operatorname{LG}(n,2n)$. First, we construct the Kausz--type compactification $\mathcal {TL}_n$ of the space of symmetric matrices and give an explicit description of its birational geometry. Second, we realize $\mathcal {TL}_n$ as a general evaluation fiber in a Kontsevich space, and then exploit this modular interpretation to derive consequences for the birational geometry of the space of pointed conics $\overline{M}_{0,1}(\operatorname{LG}(n,2n),2)$. Analogous compactifications related to orthogonal Grassmannians are also presented.

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Hanlong Fang, Alex Massarenti, Xian Wu. 2026-03-06. Compactifications of spaces of symmetric matrices and pointed Kontsevich spaces of isotropic Grassmannians. https://arxiv.org/abs/2603.05808

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