On Hilbert modular threefolds of discriminant 49

Details On Hilbert modular threefolds of discriminant 49 On Hilbert modular threefolds of discriminant 49

2011-08-08

arxiv.org/abs/1108.1820v1

Mathematics

Number Theory

Scientific paper

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)\subset Gamma = SL_2(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 P^3 with 84 isolated singular points of type A_2.

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