TL;DR
This paper proves the irrationality of the very general Verra fourfold using advanced Hodge theory and quantum cohomology techniques, marking a novel application of these methods to higher Picard rank spaces.
Contribution
It introduces a refined analysis of Hodge atoms and derives quantum multiplication matrices, applying these methods to a complex space with Picard rank greater than one for the first time.
Findings
Proves the irrationality of the very general Verra fourfold.
Develops a refined analysis of Hodge atoms based on involution.
Derives quantum multiplication matrix from quantum differential operator.
Abstract
We show that the very general Verra fourfold is irrational, using the Hodge atom framework of Katzarkov--Kontsevich--Pantev--Yu. Two novel points are: a refined analysis of Hodge atoms, based on the involution on the cohomology of , and a derivation of the quantum multiplication matrix from the quantum differential operator. This gives the first successful application of the method of Hodge atoms to a space with Picard rank greater than one.
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