A Lie theoretical construction of a Landau–Ginzburg model without projective mirrors

@article{Ballico2019ALT,
  title={A Lie theoretical construction of a Landau–Ginzburg model without projective mirrors},
  author={Edoardo Ballico and Severin Barmeier and Elizabeth Gasparim and Lino Grama and Luiz A. B. San Martin},
  journal={manuscripta mathematica},
  year={2019},
  volume={158},
  pages={85-101}
}
We describe the Fukaya–Seidel category of a Landau–Ginzburg model $$\mathrm {LG}(2)$$LG(2) for the semisimple adjoint orbit of $$\mathfrak {sl}(2, {\mathbb {C}})$$sl(2,C). We prove that this category is equivalent to a full triangulated subcategory of the category of coherent sheaves on the second Hirzebruch surface. We show that no projective variety can be mirror to $$\mathrm {LG}(2)$$LG(2), and that this remains so after compactification. 
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