Strata of k-differentials

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.

Publication Date:
Nov 16 2017
Date Submitted:
Oct 29 2018
Algebraic Geometry
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 Record created 2018-10-29, last modified 2019-04-03

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