Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks

Symmetry Integrability and Geometry-Methods and Applications

article

Hiroshi Iritani¹ 

[1] Department of Mathematics, Graduate School of Science, Kyoto University

关键词: quantum cohomology;    mirror symmetry;    toric variety;    Landau–Ginzburg model;    Gamma-integral structure;   

DOI  :  10.3842/SIGMA.2020.032

来源: National Academy of Science of Ukraine

【 摘 要 】

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 $\widehat{\Gamma}$-integral structure, to an Orlov-type semiorthogonal decomposition of topological $K$-groups. We state a conjectural functoriality of Gromov-Witten theories under discrepant transformations in terms of a Riemann-Hilbert problem.

【 授权许可】

Unknown