Pure and Applied Mathematics Quarterly

Volume 14 (2018)

Number 3-4

Unfolding of orbifold $\mathrm{LG}$ $\mathrm{B}$-models: a case study

Pages: 443 – 465

DOI: https://dx.doi.org/10.4310/PAMQ.2018.v14.n3.a2


Weiqiang He (Department of Mathematics, Sun Yat-sen University, Guangzhou, China)

Si Li (Department of Mathematical Sciences and Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)

Yifan Li (Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)


In this note we explore the variation of Hodge structures associated to the orbifold Landau–Ginzburg $\mathrm{B}$-model whose superpotential has two variables. We extend the Getzler-Gauss–Manin connection to Hochschild chains twisted by group action. As an application, we provide explicit computations for the Getzler–Gauss–Manin connection on the universal (noncommutative) unfolding of $\mathbb{Z}_2$-orbifolding of $\mathrm{A}$-type singularities. The result verifies an example of deformed version of McKay correspondence.

The work of S. Li is partially supported by grant 11801300 of NSFC and grant Z180003 of Beijing Natural Science Foundation. The work of W. He is partially supported by Tsinghua Postdoc Grant 100410019.

Received 20 April 2019

Accepted 7 May 2019

Published 5 November 2019