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arXiv · 2201.06869

Logarithmic moduli of roots of line bundles on curves

David Holmes·Giulio Orecchia
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Abstract

We use the theory of logarithmic line bundles to construct compactifications of spaces of roots of a line bundle on a family of curves, generalising work of a number of authors. This runs via a study of the torsion in the tropical and logarithmic jacobians (recently constructed by Molcho and Wise). Our moduli space carries a `double ramification cycle' measuring the locus where the given root is isomorphic to the trivial bundle, and we give a tautological formula for this class in the language of piecewise polynomial functions (as recently developed by Molcho-Pandharipande-Schmitt and Holmes-Schwarz).

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David Holmes, Giulio Orecchia. 2022-01-18. Logarithmic moduli of roots of line bundles on curves. https://doi.org/10.1016/j.exmath.2023.04.001

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