Irregular Hodge numbers of stacky Clarke mirror pairs

TL;DR

This paper establishes a duality in irregular Hodge numbers for stacky Landau-Ginzburg models, extending known results and applying to orbifold toric complete intersections and Fano stacks, with implications for degeneration behavior.

Contribution

It introduces a duality for irregular Hodge numbers in stacky mirror pairs, generalizing several prior results and applying to orbifold and toric geometries.

Findings

Proves duality of irregular Hodge numbers for stacky Landau-Ginzburg models.

Generalizes results of Batyrev--Borisov and others to broader classes.

Shows irregular Hodge numbers can be realized tropically in certain degenerations.

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.