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arXiv · 1903.07544

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

Yizhen Zhao
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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.

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Yizhen Zhao. 2019-03-18. Landau-Ginzburg/Calabi-Yau correspondence for a complete intersection via matrix factorizations. https://arxiv.org/abs/1903.07544

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