Title: Algebraic magnetism stratification of the double scalar action on the projective plane Show Chinese title

Title: 射影平面上双标量作用的代数磁性分层

Abstract: We determine the pure magnets (certain monoids) for the double scalar action of $\mathbb{G}_m^2$ on $\mathbb{P}^2$, and compute the associated attractors, yielding a canonical, fully explicit stratification. This provides a concrete non-affine example illustrating the invariants of Algebraic Magnetism. Show Chinese abstract

Abstract: 我们确定双标量作用下$\mathbb{G}_m^2$对$\mathbb{P}^2$的纯磁 (某些独异点)，并计算相关的吸引子，从而得到一个规范的、完全显式的分层结构。 这提供了一个具体的非仿射例子，说明代数磁性的不变量。