On Hilbert modular threefolds of discriminant 49
Abstract
Let K be the totally real cubic field of discriminant 49, let O be its ring of integers, and let p be the prime over 7. Let Gamma (p)⊂ Gamma = SL2(O) be the principal congruence subgroup of level p. This paper investigates the geometry of the Hilbert modular threefold attached to Gamma (p) and some related varieties. In particular, we discover an octic in P3 with 84 isolated singular points of type A2.
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