Rationally Simply Connected Hypersurfaces in Orthogonal Grassmannians
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915664089841664 |
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| author | Ghosh, Srijan |
| author_facet | Ghosh, Srijan |
| contents | In this paper, we study the moduli space of rational curves in a general low degree hypersurface in the Orthogonal Grassmanian $OG(k,n+1)$ of $k$-dimensional isotropic subspaces of an $n+1$-dimensional vector space equipped with a symmetric, non-degenerate, bilinear form. We prove rationally simply connectedness for such a general hypersurface of degree $d$ where $d$ satisfies $n+1-8k-4\ge (3k-1)d^2-d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rationally Simply Connected Hypersurfaces in Orthogonal Grassmannians Ghosh, Srijan Algebraic Geometry In this paper, we study the moduli space of rational curves in a general low degree hypersurface in the Orthogonal Grassmanian $OG(k,n+1)$ of $k$-dimensional isotropic subspaces of an $n+1$-dimensional vector space equipped with a symmetric, non-degenerate, bilinear form. We prove rationally simply connectedness for such a general hypersurface of degree $d$ where $d$ satisfies $n+1-8k-4\ge (3k-1)d^2-d$. |
| title | Rationally Simply Connected Hypersurfaces in Orthogonal Grassmannians |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.08849 |