标题： 相对零的仿射不变子流形的Siegel--Veech常数的面积 显示英文标题

标题： Area Siegel--Veech constants for affine invariant submanifolds of REL zero

摘要： 我们用阿贝尔微分层的多尺度紧化中零点阶数指定的水平图来描述任意仿射不变子流形相对于REL零主边界的几何结构。 我们证明了仿射不变子流形的面积Siegel–Veech常数可以通过主边界层的体积来获得。 作为应用，我们证明了[CMS23a]中的猜想公式，该公式通过交叉理论计算了REL零情况下的面积Siegel–Veech常数。 特别是，该公式对于具有奇数零点阶数的二次微分层以及哥特族位置成立。 我们还明确描述了哥特族位置的主边界分量及其对面积Siegel–Veech常数的个体贡献。 显示英文摘要

摘要： We describe the principal boundary of an arbitrary affine invariant submanifold of REL zero in terms of level graphs of the multi-scale compactification of strata of Abelian differentials with prescribed orders of zeros. We show that the area Siegel--Veech constant of the affine invariant submanifold can be obtained by using volumes of the principal boundary strata. As an application, we prove the conjectural formula in [CMS23a] that computes the area Siegel--Veech constant via intersection theory in the case of REL zero. In particular, the formula holds for strata of quadratic differentials with odd orders of zeros and for the gothic locus. We also explicitly describe the principal boundary components of the gothic locus and their individual contributions to the area Siegel--Veech constant