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arXiv · 2609.06541

Disconnectedness of the Hilbert Schemes of $E_6/P_6$

Minyoung Jeon
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Abstract

In this note, we show that the Hilbert scheme $\text{Hilb}_{P_{d,4}(t)}(E_6/P_6)$ associated with the Hilbert polynomial $P_{d,4}(t)$ is disconnected by determining that it has exactly two connected components. This result adapts Seong's methods, successfully extending the disconnectedness of Grassmannians to the exceptional type $E_6$.

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Minyoung Jeon. 2026-09-06. Disconnectedness of the Hilbert Schemes of $E_6/P_6$. https://arxiv.org/abs/2609.06541

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