Nested Hilbert Schemes on Hirzebruch surfaces and quiver varieties

Ugo Bruzzo, Valeriano Lanza, Pedro H. Dos Santos

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…