Symplectomorphism group relations and degenerations of Landau-Ginzburg models

Colin Diemer, Ludmil Katzarkov, Gabriel Kerr

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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 B-model mirror to these degenerations, which gives a new mirror symmetry approach to the minimal model program.

Original languageEnglish (US)
Pages (from-to)2167-2171
Number of pages5
JournalJournal of the European Mathematical Society
Volume18
Issue number10
DOIs
StatePublished - 2016

Keywords

  • Homological mirror symmetry
  • Landau-Ginzburg models
  • Minimal model program
  • Symplectomorphisms
  • Toric varieties

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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