Hurwitz ball quotients View Full Text


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Article Info

DATE

2014-10

AUTHORS

Matthew Stover

ABSTRACT

We consider the analogue of Hurwitz curves, smooth projective curves C of genus g≥2 that realize equality in the Hurwitz bound |Aut(C)|≤84(g-1), to smooth compact quotients S of the unit ball in C2. When S is arithmetic, we show that |Aut(S)|≤288e(S), where e(S) is the (topological) Euler characteristic, and in the case of equality show that S 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 2-orbifold. More... »

PAGES

75-91

References to SciGraph publications

  • 2016-03. New non-arithmetic complex hyperbolic lattices in INVENTIONES MATHEMATICAE
  • 1985. Manifolds of non positive curvature in ARBEITSTAGUNG BONN 1984
  • 1986-12. Monodromy of hypergeometric functions and non-lattice integral monodromy in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • 1986-12. Generalized picard lattices arising from half-integral conditions in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • 1983. Arrangements of Lines and Algebraic Surfaces in ARITHMETIC AND GEOMETRY
  • 1989-12. Volumes of S-arithmetic quotients of semi-simple groups in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • 2007-05. Fake projective planes in INVENTIONES MATHEMATICAE
  • 1975-10. Some analytic estimates of class numbers and discriminants in INVENTIONES MATHEMATICAE
  • 2000-05. The Leech lattice and complex hyperbolic reflections in INVENTIONES MATHEMATICAE
  • Journal

    TITLE

    Mathematische Zeitschrift

    ISSUE

    1-2

    VOLUME

    278

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00209-014-1306-6

    DOI

    http://dx.doi.org/10.1007/s00209-014-1306-6

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1044559263


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