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Mathematics > Algebraic Geometry
Title: Nested Hilbert Schemes on Hirzebruch surfaces and quiver varieties
(Submitted on 26 Mar 2024 (v1), last revised 8 May 2024 (this version, v2))
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.
Submission history
From: Ugo Bruzzo [view email][v1] Tue, 26 Mar 2024 20:57:52 GMT (30kb,D)
[v2] Wed, 8 May 2024 16:32:08 GMT (30kb,D)
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