Laurent polynomials in mirror symmetry

why and how?


  • A. Kasprzyk University of Nottingham.
  • V. Przyjalkowski Steklov Mathematical Institute of Russian Academy of Sciences.



mirror symmetry, Landau–Ginzburg model, Fano variety, log Calabi–Yau, toric degeneration, Hodge numbers


We survey the approach to mirror symmetry via Laurent polynomials, outlining some of the main conjectures, problems, and questions related to the subject. We discuss: how to construct Landau–Ginzburg models for Fano varieties; how to apply them to classification problems; and how to compute invariants of Fano varieties via Landau–Ginzburg models.

Author Biography

A. Kasprzyk, University of Nottingham.

School of Mathematical Sciences.


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How to Cite

A. Kasprzyk and V. Przyjalkowski, “Laurent polynomials in mirror symmetry: why and how?”, Proyecciones (Antofagasta, On line), vol. 41, no. 2, pp. 481-515, Mar. 2022.