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EIGENPERIODS AND THE MODULI OF POINTS IN THE LINE
Published online by Cambridge University Press: 24 February 2025
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.
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- © The Author(s), 2025. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal
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