Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks
arXiv:1906.00801 · doi:10.3842/SIGMA.2020.032
Abstract
We introduce a global Landau-Ginzburg model which is mirror to several toric Deligne-Mumford stacks and describe the change of the Gromov-Witten theories under discrepant transformations. We prove a formal decomposition of the quantum cohomology D-modules (and of the all-genus Gromov-Witten potentials) under a discrepant toric wall-crossing. In the case of weighted blowups of weak-Fano compact toric stacks along toric centres, we show that an analytic lift of the formal decomposition corresponds, via the -integral structure, to an Orlov-type semiorthogonal decomposition of topological -groups. We state a conjectural functoriality of Gromov-Witten theories under discrepant transformations in terms of a Riemann-Hilbert problem.
arXiv comment111 pages, 16 figures, published version
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