Geodesic
Quasimaps to moduli spaces of sheaves
Forum of Mathematics, Pi, Tome 13 (2025) no. 1, p. e12

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We develop a theory of quasimaps to a moduli space of sheaves M on a surface S. Under some assumptions, we prove that moduli spaces of quasimaps are proper and carry a perfect obstruction theory. Moreover, they are naturally isomorphic to moduli spaces of sheaves on threefolds $S\times C$, where C is a nodal curve. Using Zhou’s theory of entangled tails, we establish a wall-crossing formula which therefore relates the Gromov–Witten theory of M and the Donaldson–Thomas theory of $S\times C$ with relative insertions. We evaluate the wall-crossing formula for Hilbert schemes of points $S^{[n]}$, if S is a del Pezzo surface. 
Nesterov, Denis. Quasimaps to moduli spaces of sheaves. Forum of Mathematics, Pi, Tome 13 (2025) no. 1, p. e12. doi: 10.1017/fmp.2025.3
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