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arXiv · 1907.06569

Connected Components in the Hilbert Scheme of hypersurfaces in Grassmannians

See-Hak Seong
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Abstract

We show that when $d \geq 3$, the Hilbert scheme $Hilb_{dT+1-\binom{d-1}{2}}(G(k,n))$ has 2 components, even though elements in both components have the same cohomology class. Moreover, we show that the Hilbert scheme associated to the Hilbert polynomial $\binom{T+n}{n}-\binom{T+n-d}{n}$ in Grassmannian has at most 2 connected components.

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See-Hak Seong. 2019-07-16. Connected Components in the Hilbert Scheme of hypersurfaces in Grassmannians. https://arxiv.org/abs/1907.06569

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