Compactifications of spaces of symmetric matrices and pointed Kontsevich spaces of isotropic Grassmannians
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910042972749824 |
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| author | Fang, Hanlong Massarenti, Alex Wu, Xian |
| author_facet | Fang, Hanlong Massarenti, Alex Wu, Xian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05808 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Compactifications of spaces of symmetric matrices and pointed Kontsevich spaces of isotropic Grassmannians Fang, Hanlong Massarenti, Alex Wu, Xian Algebraic Geometry 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. |
| title | Compactifications of spaces of symmetric matrices and pointed Kontsevich spaces of isotropic Grassmannians |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2603.05808 |