Symplectomorphism group relations and degenerations of Landau–Ginzburg models

  • Colin Diemer

    University of Miami, Coral Gables, USA
  • Ludmil Katzarkov

    University of Miami, Coral Gables, USA
  • Gabriel Kerr

    Kansas State University, Manhattan, USA

Abstract

We describe explicit relations in the symplectomorphism groups of hypersurfaces in toric stacks. To define the elements involved, we construct a proper stack of these hypersurfaces whose boundary represents stable pair degenerations. Our relations arise through the study of the one-dimensional strata of this stack. The results are then examined from the perspective of homological mirror symmetry where we view sequences of relations as maximal degenerations of Landau–Ginzburg models. We then study the -model mirror to these degenerations, which gives a new mirror symmetry approach to the minimal model program.

Cite this article

Colin Diemer, Ludmil Katzarkov, Gabriel Kerr, Symplectomorphism group relations and degenerations of Landau–Ginzburg models. J. Eur. Math. Soc. 18 (2016), no. 10, pp. 2167–2271

DOI 10.4171/JEMS/640