English

Landau-Ginzburg/Calabi-Yau correspondence for a complete intersection via matrix factorizations

Algebraic Geometry 2019-03-20 v1 High Energy Physics - Theory

Abstract

By generalizing the Landau-Ginzburg/Calabi-Yau correspondence for hypersurfaces, we can relate a Calabi-Yau complete intersection to a hybrid Landau-Ginzburg model: a family of isolated singularities fibered over a projective line. In recent years Fan, Jarvis, and Ruan have defined quantum invariants for singularities of this type, and Clader and Clader-Ross have provided a equivalence between these invariants and Gromov-Witten invariants of complete intersections. For Calabi-Yau complete intersections of two cubics, we show that this equivalence is directly related - via Chen character - to the equivalences between the derived category of coherent sheaves and that of matrix factorizations of the singularities. This generalizes Chiodo-Iritani-Ruan's theorem matching Orlov's equivalences and quantum LG/CY correspondence for hypersurfaces.

Keywords

Cite

@article{arxiv.1903.07544,
  title  = {Landau-Ginzburg/Calabi-Yau correspondence for a complete intersection via matrix factorizations},
  author = {Yizhen Zhao},
  journal= {arXiv preprint arXiv:1903.07544},
  year   = {2019}
}