论文标题
线性次级的边界
The boundary of linear subvarieties
论文作者
论文摘要
我们描述了在多尺度差异的模量空间中线性亚变化的边界。线性亚变化是（可能是）Meromormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormorthic差异的次数，在当地坐标是由线性方程式给出的。此类的主要例子是仿射不变的子曼尼福德，即$ \ operatatorName {sl}（2，\ mathbb {r}）$ orbits的关闭。我们证明，任何线性亚变量的边界再次由边界的广义周期坐标中的线性方程式给出。我们的主要技术工具是对多尺度差速器模量空间边界附近的时期进行的渐近分析，该时期产生了独立关注的进一步技术和结果。
We describe the boundary of linear subvarieties in the moduli space of multi-scale differentials. Linear subvarieties are algebraic subvarieties of strata of (possibly) meromorphic differentials that in local period coordinates are given by linear equations. The main example of such are affine invariant submanifolds, that is, closures of $\operatorname{SL}(2,\mathbb{R})$-orbits. We prove that the boundary of any linear subvariety is again given by linear equations in generalized period coordinates of the boundary. Our main technical tool is an asymptotic analysis of periods near the boundary of the moduli space of multi-scale differentials which yields further techniques and results of independent interest.
