A brief survey of FJRW theory. (English) Zbl 1452.14056

Hori, Kentaro (ed.) et al., Primitive forms and related subjects – Kavli IPMU 2014. Proceedings of the international conference, University of Tokyo, Tokyo, Japan, February 10–14, 2014. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 83, 19-53 (2019).
Summary: In this paper we describe some of the constructions of FJRW theory. We also briefly describe its relation to Saito-Givental theory via Landau-Ginzburg mirror symmetry and its relation to Gromov-Witten theory via the Landau-Ginzburg/Calabi-Yau correspondence. We conclude with a discussion of some of the recent results in the field, including the gauged linear sigma model, which is expected to provide a geometric framework for unifying many of these ideas.
For the entire collection see [Zbl 1446.53004].


14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
32S05 Local complex singularities
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
35Q53 KdV equations (Korteweg-de Vries equations)
14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry
Full Text: DOI arXiv Euclid


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