A Landau–Ginzburg mirror theorem via matrix factorizations

For an invertible quasihomogeneous polynomial we prove an all-genus mirror theorem relating two cohomological field theories of Landau–Ginzburg type. On the -side it is the Saito–Givental theory for a specific choice of a primitive form. On the -side, it is the matrix factorization CohFT for the dua...

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Bibliographic Details
Published inJournal für die reine und angewandte Mathematik Vol. 2023; no. 794; pp. 55 - 100
Main Authors He, Weiqiang, Polishchuk, Alexander, Shen, Yefeng, Vaintrob, Arkady
Format Journal Article
LanguageEnglish
Published De Gruyter 01.01.2023
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Summary:For an invertible quasihomogeneous polynomial we prove an all-genus mirror theorem relating two cohomological field theories of Landau–Ginzburg type. On the -side it is the Saito–Givental theory for a specific choice of a primitive form. On the -side, it is the matrix factorization CohFT for the dual singularity with the maximal diagonal symmetry group.
ISSN:0075-4102
1435-5345
DOI:10.1515/crelle-2022-0057