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Irregular Hodge numbers of stacky Clarke mirror pairs

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arxiv 2408.09016 v2 pith:XM4HHTF2 submitted 2024-08-16 math.AG

classification math.AG
keywords provehodgeresultsirregularorbifoldclarkecohomologycomplete
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We prove a duality between the graded pieces of the irregular Hodge filtration on the twisted cohomology for a large class of Clarke mirror pairs of stacky Landau-Ginzburg models. We use this to recover results of Batyrev--Borisov, generalize results of Ebeling-Gusein-Zade-Takahashi and Krawitz, and prove results similar to those of Gross-Katzarkov-Ruddat. We apply our results to prove a generalized version of a conjecture of Katzarkov-Kontsevich-Pantev for orbifold toric complete intersections with nef anticanonical divisors and orbifold Fano stacks, and we prove the Hodge number duality result for orbifold log Calabi-Yau complete intersections. Along the way, we study the behaviour of twisted cohomology under degeneration and prove that for certain degenerations of toric Landau--Ginzburg models, irregular Hodge numbers admit a tropical realization.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. $E_1$-Degeneration for Irregular Hodge Filtrations on Deligne--Mumford Stacks

    math.AG 2026-08 accept novelty 7.0 of 10

    For every smooth separated Deligne-Mumford stack with quasi-projective coarse space, the irregular Hodge filtration degenerates at E1 on every good stack compactification.

  2. Compactification Independence of the Irregular Hodge Filtration on Deligne-Mumford Stacks

    math.AG 2026-08 conditional novelty 7.0 of 10

    Compactification independence of the irregular Hodge filtration is proven for Deligne-Mumford stacks, and the resulting orbifold irregular Hodge numbers become invariants of the stacky Landau-Ginzburg model.

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