PERIODS IN FAMILIES AND DERIVATIVES OF PERIOD MAPS
Abstract
Abstract Given a smooth proper family f : X → S $f:X\rightarrow S$ f colon upper X right arrow upper S , we study the (quasi)-periods of the fibres of f as (germs of) functions on S . We show that the field they generate has the same algebraic closure as that given by the flag variety coordinates parametrizing the corresponding Hodge filtration, together with their derivatives. Moreover, in the more general context of an arbitrary flat vector bundle, we determine the transcendence degree of the function field generated by the flat coordinates of algebraic sections. Our results are inspired by and generalize work of Bertrand–Zudilin.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Differential Equations and Dynamical Systems
Cellular Automata and Applications
Publication details
- Journal / source
- Journal of the Institute of Mathematics of Jussieu
- Publisher
- Cambridge University Press (CUP)
- Volume
- 25
- Issue
- 6
- Pages
- 1–20
- Publication date
- 12 August 2026
- Language
- EN