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    Hurwitz ball quotients

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    Genre
    Journal Article
    Date
    2014-01-01
    Author
    Stover, M
    Subject
    math.GT
    math.GT
    math.AG
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/5916
    
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    DOI
    10.1007/s00209-014-1306-6
    Abstract
    © 2014, Springer-Verlag Berlin Heidelberg. We consider the analogue of Hurwitz curves, smooth projective curves (Formula Presented) of genus (Formula Presented) that realize equality in the Hurwitz bound (Formula Presented), to smooth compact quotients (Formula Presented) of the unit ball in (Formula Presented). When (Formula Presented) is arithmetic, we show that (Formula Presented), where (Formula Presented) is the (topological) Euler characteristic, and in the case of equality show that (Formula Presented) is a regular cover of a particular Deligne–Mostow orbifold. We conjecture that this inequality holds independent of arithmeticity, and note that work of Xiao makes progress on this conjecture and implies the best-known lower bound for the volume of a complex hyperbolic (Formula Presented)-orbifold.
    Citation to related work
    Springer Science and Business Media LLC
    Has part
    Mathematische Zeitschrift
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    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/5898
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