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arXiv · 2403.18099

Nested Hilbert Schemes on Hirzebruch surfaces and quiver varieties

Ugo Bruzzo·Valeriano Lanza·Pedro H. Dos Santos
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Abstract

For $n\ge 1$ we show that the length 1 nested Hilbert scheme of the total space $X_n$ of the line bundle $\mathcal O_{\mathbb P^1}(-n)$, parameterizing pairs of nested 0-cycles in $X_n$, is a quiver variety associated with a suitable quiver with relations. This generalizes previous work about nested Hilbert schemes on $\mathbb C^2$ in one direction, and about the Hilbert schemes of points of $X_n$ in another direction.

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Ugo Bruzzo, Valeriano Lanza, Pedro H. Dos Santos. 2024-03-26. Nested Hilbert Schemes on Hirzebruch surfaces and quiver varieties. https://arxiv.org/abs/2403.18099

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