Mixed Hodge numbers and factorial ratios
Abstract
This note is an extended version of the slides for my talk with the same title at the Arithmetic, geometry, and modular forms: a conference in honour of Bill Duke in June 2019 at the ETH in Z"urich. The results presented concern three geometric criteria for the integrality of factorial ratios, numbers such as (30n)!n!/(6n)!(10n)!(15n)!, which are integral in a non-immediate way for all n. This work is an offshoot of an ongoing project on hypergeometric motives joint with D. Roberts and M. Watkins.
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