Logarithmic moduli of roots of line bundles on curves
arXiv:2201.06869 · doi:10.1016/j.exmath.2023.04.001
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).
27 pages. Very close to published version. Comments still very welcome!