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arXiv · 2112.12891

Degenerations, fibrations and higher rank Landau-Ginzburg models

Charles F. Doran·Jordan Kostiuk·Fenglong You
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Abstract

We study semi-stable degenerations of quasi-Fano varieties to unions of two pieces. We conjecture that the higher rank Landau-Ginzburg models mirror to these two pieces can be glued together to lower rank Landau-Ginzburg models which are mirror to the original quasi-Fano varieties. We prove this conjecture by relating their Euler characteristics, generalized functional invariants as well as periods. We also use it to conjecture a relation between the degenerations to the normal cones and the fibrewise compactifications of higher rank Landau-Ginzburg models. Furthermore, we use it to iterate the Doran-Harder-Thompson conjecture and obtain higher codimension Calabi-Yau fibrations.

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Charles F. Doran, Jordan Kostiuk, Fenglong You. 2021-12-24. Degenerations, fibrations and higher rank Landau-Ginzburg models. https://arxiv.org/abs/2112.12891

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