Strata of $k$-differentials
Algebraic Geometry
2017-11-17 v2 Dynamical Systems
Geometric Topology
Abstract
A -differential on a Riemann surface is a section of the -th power of the canonical line bundle. Loci of -differentials with prescribed number and multiplicities of zeros and poles form a natural stratification of the moduli space of -differentials. In this paper we give a complete description for the compactification of the strata of -differentials in terms of pointed stable -differentials, for all . The upshot is a global -residue condition that can also be reformulated in terms of admissible covers of stable curves. Moreover, we study properties of -differentials regarding their deformations, residues, and flat geometric structure.
Keywords
Cite
@article{arxiv.1610.09238,
title = {Strata of $k$-differentials},
author = {Matt Bainbridge and Dawei Chen and Quentin Gendron and Samuel Grushevsky and Martin Moeller},
journal= {arXiv preprint arXiv:1610.09238},
year = {2017}
}
Comments
corrected and updated; final version, to appear in Algebraic Geometry