Hurwitz ball quotients
نویسنده
چکیده
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 C. 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.
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