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arXiv · 2502.11704

Motivic counting of rational curves with tangency conditions via universal torsors

Loïs Faisant
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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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Loïs Faisant. 2025-02-17. Motivic counting of rational curves with tangency conditions via universal torsors. https://arxiv.org/abs/2502.11704

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