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Corpus ID: 119655261

Fields of definition of curves of a given degree

@article{Holmes2019FieldsOD,
title={Fields of definition of curves of a given degree},
author={D. Holmes and Nick Rome},
journal={arXiv: Algebraic Geometry},
year={2019}
}

Kontsevich and Manin gave a formula for the number $N_e$ of rational plane curves of degree $e$ through $3e-1$ points in general position in the plane. When these $3e-1$ points have coordinates in the rational numbers, the corresponding set of $N_e$ rational curves has a natural Galois-module structure. We make some extremely preliminary investigations into this Galois module structure, and relate this to the deck transformations of the generic fibre of the product of the evaluation maps on the… CONTINUE READING