Moduli Space of Cubic Surfaces as Ball Quotient via Hypergeometric Functions

نویسنده

  • Brent R. Doran
چکیده

We describe hypergeometric functions of Deligne-Mostow type for open subsets of the configuration space of six points on P, induced from those for seven points on P. The seven point ball quotient example DM(2, 1) does not appear on Mostow’s original list [9], but does appear on Thurston’s corrected version [12]. We show that DM(2, 1) is a finite cover of the moduli space of cubic surfaces MC endowed with the ball quotient structure ΓC\B 4 of [2]. This answers a question of Allcock [1] about the commensurability of ΓC with the monodromy groups of Deligne-Mostow hypergeometric functions.

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تاریخ انتشار 2004