Sanda–Shamoto's Dubrovin conjecture for Fano manifolds

Let XX be a Fano manifold. An irregular perverse schober is understood here as the categorical structure whose nearby cycle and Hochschild decategorification are specified below.

Sanda–Shamoto's Dubrovin conjecture. There exists an irregular perverse schober whose nearby cycle is Db(X)D^b(X) and whose Hochschild decategorification gives Stokes data that is the irregular Riemann–Hilbert image of the quantum D\operatorname{D}-module of XX around 0P10\in \mathbb{P}^1_\hbar.

This conjecture proposes a categorical enhancement of the relationship between quantum D\operatorname{D}-modules, Stokes structures, and semiorthogonal decompositions in the setting of Dubrovin's conjecture. The supplied text gives no evidence that it has been resolved.

Sources & referencesView supporting material

Primary source

Tatsuki Kuwagaki, “Categorification of Legendrian knots”, arXiv:1902.04269 (2019).

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