@unpublished{19055,
  abstract     = {Using the formalism of Cox rings and universal torsors, we prove a decomposition of the Grothendieck motive of the moduli space of morphisms from an arbitrary smooth projective curve to a Mori Dream Space (MDS).
 For the simplest cases of MDS, that of toric varieties, we use this decomposition to prove an instance of the motivic Batyrev--Manin--Peyre principle for curves satisfying tangency conditions with respect to the boundary divisors, often called Campana curves.},
  author       = {Faisant, Loïs},
  booktitle    = {arXiv},
  title        = {{Motivic counting of rational curves with tangency conditions via universal torsors}},
  doi          = {10.48550/ARXIV.2502.11704},
  year         = {2025},
}