title: Hilbert modular threefolds of arithmetic genus one
abstract: D. Weisser (1981) proved that there are exactly four Galois cubic number fields with Hilbert modular threefolds of arithmetic genus one. In this paper, we extend Weisser's work to cover all cubic number fields. Our main result is that there are exactly 33 fields with Hilbert modular threefolds of arithmetic genus one. These fields are enumerated explicitly
keyphrases: Hilbert modular threefolds arithmetic genus one Galois cubic number fields