Strata of k-differentials [article]

M. Bainbridge, D. Chen, Q. Gendron, S. Grushevsky, M. Möller, University, My, University, My
2020
A k-differential on a Riemann surface is a section of the kth 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
more » ... issible covers of stable curves. Moreover, we study properties of k-differentials regarding their deformations, residues, and at geometric structure. © Foundation Compositio Mathematica 2019.
doi:10.15488/9761 fatcat:73p57jdlx5h2vetrz3olwb5nca