English

On Hilbert modular threefolds of discriminant 49

Number Theory 2011-08-10 v1 Algebraic Geometry

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)\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.

Keywords

Cite

@article{arxiv.1108.1820,
  title  = {On Hilbert modular threefolds of discriminant 49},
  author = {Lev A. Borisov and Paul E. Gunnells},
  journal= {arXiv preprint arXiv:1108.1820},
  year   = {2011}
}