标题： 通过通用扭矩对具有相切条件的有理曲线进行动机计数 显示英文标题

标题： Motivic counting of rational curves with tangency conditions via universal torsors

摘要： 利用Cox环和万有挠场的形式化语言，我们证明了模空间的Grothendieck动机的一种分解，该模空间由任意光滑射影曲线到Mori Dream Space (MDS) 的态射组成。 对于MDS的最简单情形，即toric簇的情形，我们利用这一分解证明了motivic Batyrev--Manin--Peyre原理的一个实例，适用于满足与边界除子相切条件的曲线，通常称为Campana曲线。 显示英文摘要

摘要： 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.