Categorical DT flop invariance at the zero wall

Let Pn(X,β)εP_n(X,\beta)_{\varepsilon} and Pn(X,β)εP_n(X,\beta)_{-\varepsilon} be the stable-pair moduli spaces for parameters on the two sides of the wall at t0=0t_0=0, with 0<ε10<\varepsilon\ll1. Categorical DT zero-wall flop conjecture. There exists an equivalence

DTC(Pn(X,β)ε)DTC(Pn(X,β)ε).\mathcal{DT}^{\mathbb{C}^{\ast}}(P_n(X,\beta)_{\varepsilon})\simeq\mathcal{DT}^{\mathbb{C}^{\ast}}(P_n(X,\beta)_{-\varepsilon}).

The conjecture reflects the d-critical flop at the zero wall and predicts categorical DT invariance across it; the source does not give a resolution.

Sources & referencesView supporting material

Primary source

Yukinobu Toda, “Categorical Donaldson-Thomas theory for local surfaces”, arXiv:1907.09076 (2021).

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