Eigenperiods and the moduli of points in the line
Algebraic Geometry
2025-10-01 v2
Abstract
We study the period map of configurations of n points on the projective line constructed via a cyclic cover branching along these points. By considering the decomposition of its Hodge structure into eigenspaces, we establish the codimension of the locus where the eigenperiod map is still pure. Furthermore, we show that the period map extends to the divisors of a specific moduli space of weighted stable rational curves, and that this extension satisfies a local Torelli map along its fibers.
Cite
@article{arxiv.2311.09352,
title = {Eigenperiods and the moduli of points in the line},
author = {Haohua Deng and Patricio Gallardo},
journal= {arXiv preprint arXiv:2311.09352},
year = {2025}
}
Comments
26 pages, To appear in Nagoya. Math. J