Strata of $k$-differentials
Strata of $k$-differentials
复制标题
$k$-差异层
作者：
Matt Bainbridge;Dawei Chen;Q. Gendron;S. Grushevsky;Martin Moeller
黎曼曲面上的k-微分是标准线丛的k次幂的一个截面。具有指定数目的$k$-微分的轨迹和零点和极点的重数形成了$k$-微分的模空间的自然分层。在本文中，我们给出了一个完整的描述层的$k$-微分紧化的点稳定的$k $-微分，对所有的$k$。其结果是一个全球性的$k$-残留条件，也可以重新制定的容许覆盖稳定曲线。此外，我们研究的性质$k$-微分关于他们的变形，残留物，和平坦的几何结构。
A $k$-differential on a Riemann surface is a section of the $k$-th power of the canonical line bundle. Loci of $k$-differentials with prescribed number and multiplicities of zeros and poles form a natural stratification of the moduli space of $k$-differentials. In this paper we give a complete description for the compactification of the strata of $k$-differentials in terms of pointed stable $k$-differentials, for all $k$. The upshot is a global $k$-residue condition that can also be reformulated in terms of admissible covers of stable curves. Moreover, we study properties of $k$-differentials regarding their deformations, residues, and flat geometric structure.
影响因子：
2.5
作者：
Matt Bainbridge;Dawei Chen;Q. Gendron;S. Grushevsky;Martin Moeller
通讯作者：
Matt Bainbridge;Dawei Chen;Q. Gendron;S. Grushevsky;Martin Moeller