Hilbert modular varieties of Galois quartic fields

[摘要] Let k be a totally real number field of degree n over Q with ring of integers O-k. The Hilbert modular variety of k is a desingularization of the (natural) compactification of PSL(2)(O-k)\H-n. This paper focuses on Hilbert modular varieties of Galois quartic fields containing units of norm -1. The main result is that each of these varieties has arithmetic genus greater than one and hence is not rational. (C) 1997 Academic Press.

[发布日期] 1997-03-01