Divisors and curves on logarithmic mapping spaces. (English) Zbl 07896248
Summary: We determine the rational class and Picard groups of the moduli space of stable logarithmic maps in genus zero, with target projective space relative a hyperplane. For the class group we exhibit an explicit basis consisting of boundary divisors. For the Picard group we exhibit a spanning set indexed by piecewise-linear functions on the tropicalisation. In both cases a complete set of boundary relations is obtained by pulling back the WDVV relations from the space of stable curves. Our proofs hinge on a controlled technique for manufacturing test curves in logarithmic mapping spaces, opening up the topology of these spaces to further study.
MSC:
| 14H10 | Families, moduli of curves (algebraic) |
| 14C20 | Divisors, linear systems, invertible sheaves |
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