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Fundamental Matrix Factorization in the FJRW-Theory Revisited

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Abstract

We present an improved construction of the fundamental matrix factorization in the FJRW-theory given in Polishchuk and Vaintrob (J Reine Angew Math 714:1–22, 2016). The revised construction makes the independence on choices more apparent and works for a possibly nonabelian finite group of symmetries. One of the new ingredients is the category of dg-matrix factorizations over a dg-scheme.

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Acknowledgements

I am grateful to Felix Janda and Yongbin Ruan for organizing the RTG Conference on Witten’s r-spin class and related topics in January 2017, where the results of this note were first presented. I also thank Institut Mathematique Jussieu and Institut des Hautes Etudes Scientifiques for hospitality and excellent working conditions during preparation of this paper.

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Authors and Affiliations

  1. University of Oregon, Eugene, OR, USA

    Alexander Polishchuk

  2. National Research University Higher School of Economics, Moscow, Russia

    Alexander Polishchuk

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  1. Alexander Polishchuk
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Correspondence to Alexander Polishchuk.

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To Rafail Kalmanovich Gordin, with gratitude.

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Supported in part by the NSF Grant DMS-1700642 and by the Russian Academic Excellence Project ‘5-100’.

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Polishchuk, A. Fundamental Matrix Factorization in the FJRW-Theory Revisited. Arnold Math J. 5, 23–35 (2019). https://doi.org/10.1007/s40598-019-00100-3

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  • DOI: https://doi.org/10.1007/s40598-019-00100-3

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