Symplectomorphism group relations and degenerations of Landau–Ginzburg models
Colin Diemer
University of Miami, Coral Gables, USALudmil Katzarkov
University of Miami, Coral Gables, USAGabriel 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