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arXiv · 2512.08849

Rationally Simply Connected Hypersurfaces in Orthogonal Grassmannians

Srijan Ghosh
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Abstract

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 $n+1-8k-4\ge (3k-1)d^2-d$.

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Srijan Ghosh. 2025-12-09. Rationally Simply Connected Hypersurfaces in Orthogonal Grassmannians. https://arxiv.org/abs/2512.08849

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