Sukjoo Lee - Generalization of the DHT mirror construction and mirror P=W conjectures - 13.06.2023

Hodge theory, Mirror Symmetry, and Physics of Calabi-Yau Moduli
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A MATCH-PIMS-STRUCTURES workshop in Mathematical Physics, held from June 12 to 16, 2023, at the Mathematikon in Heidelberg
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Abstract: We discuss how to extend the Doran-Harder-Thompson (DHT) mirror construction in case of some higher type degenerations of a Calabi-Yau manifold X. One of the key ingredients is a higher rank Landau-Ginzburg (LG) model, a multi-potential analogue of the ordinary LG model that will describe a mirror of each component in the degeneration fiber. They can be glued to produce a mirror Calabi-Yau Y with a Calabi-Yau fibration structure. Moreover, the perverse Leray filtration associated to this fibration is predicted to be mirror to the monodromy weight filtration in the degeneration of X. We explain how this “P=W” type phenomenon is related with another mirror P=W, introduced by Harder-Katzarkov-Przyjalkowski, for the mirrors of components of the degeneration fiber.