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.
Irregular Hodge numbers of stacky Clarke mirror pairs
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abstract
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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Compactification Independence of the Irregular Hodge Filtration on Deligne-Mumford Stacks
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.