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arXiv · 1610.09238

Strata of $k$-differentials

Matt Bainbridge·Dawei Chen·Quentin Gendron·Samuel Grushevsky·Martin Moeller
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Abstract

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.

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Matt Bainbridge, Dawei Chen, Quentin Gendron, Samuel Grushevsky, Martin Moeller. 2016-10-28. Strata of $k$-differentials. https://arxiv.org/abs/1610.09238

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