Motivic counting of rational curves with tangency conditions via universal torsors
Faisant L. Motivic counting of rational curves with tangency conditions via universal torsors. arXiv, 2502.11704.
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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.
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Date Published
2025-02-17
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arXiv
Acknowledgement
The author acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413.
Article Number
2502.11704
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Cite this
Faisant L. Motivic counting of rational curves with tangency conditions via universal torsors. arXiv. doi:10.48550/ARXIV.2502.11704
Faisant, L. (n.d.). Motivic counting of rational curves with tangency conditions via universal torsors. arXiv. https://doi.org/10.48550/ARXIV.2502.11704
Faisant, Loïs. “Motivic Counting of Rational Curves with Tangency Conditions via Universal Torsors.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2502.11704.
L. Faisant, “Motivic counting of rational curves with tangency conditions via universal torsors,” arXiv. .
Faisant L. Motivic counting of rational curves with tangency conditions via universal torsors. arXiv, 2502.11704.
Faisant, Loïs. “Motivic Counting of Rational Curves with Tangency Conditions via Universal Torsors.” ArXiv, 2502.11704, doi:10.48550/ARXIV.2502.11704.
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