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Strata of k-differentials

MPS-Authors
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Bainbridge,  Matt
Max Planck Institute for Mathematics, Max Planck Society;

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Chen,  Dawei
Max Planck Institute for Mathematics, Max Planck Society;

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Gendron,  Quentin
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons235370

Grushevsky,  Samuel
Max Planck Institute for Mathematics, Max Planck Society;

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Möller,  Martin
Max Planck Institute for Mathematics, Max Planck Society;

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引用

Bainbridge, M., Chen, D., Gendron, Q., Grushevsky, S., & Möller, M. (2019). Strata of k-differentials. Algebraic Geometry, 6(2), 196-233. doi:10.14231/AG-2019-011.


引用: https://hdl.handle.net/21.11116/0000-0004-40D1-7
要旨
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 admissible covers of stable curves. Moreover, we study properties of
k-differentials regarding their deformations, residues, and flat geometric structure.