Symplectomorphism group relations and degenerations of Landau-Ginzburg models

Details Symplectomorphism group relations and degenerations of Landau-Ginzburg models Symplectomorphism group relations and degenerations of Landau-Ginzburg models

2012-04-10

arxiv.org/abs/1204.2233v1

Mathematics

Symplectic Geometry

68 pages, 15 figures

Scientific paper

In this paper, we describe explicit relations in the symplectomorphism groups of toric hypersurfaces. To define the elements involved, we construct a proper stack of toric hypersurfaces with compactifying boundary representing toric hypersurface 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 B-model mirror to these degenerations, which gives a new mirror symmetry approach to the minimal model program.

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