Work

Eigenperiods and the Moduli of Points in the Line

Year: 2025

Type: article

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.

Source: Nagoya Mathematical Journal

DOI: 10.1017/nmj.2025.7

Authors: HAOHUA DENG, PATRICIO GALLARDO

Institutions: Duke University, University of California, Riverside

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Washington University in St. Louis

Award: LEAPS-MPS: Describing Compactifications of Moduli Spaces of Varieties and Pairs.