Quotients of abelian varieties by reflection groups

Abstract

We prove (by a case-by-case analysis) a conjecture of Bernstein/Schwarzman to the effect that quotients of abelian varieties by suitable actions of (complex) reflection groups are weighted projective spaces, and show that this remains true after reduction to finite characteristic (including characteristics dividing the order of the group!). We also show that an analogous statement holds (with five explicitly enumerated exceptions) for actions of quaternionic reflection groups on supersingular abelian varieties.

77 pages LaTeX, 7 tables. v2: clarifies the (lack of) dependence on Popov's classification; adds some references to recent results on special cases

Cited by in corpus (1)

• Discrete complex reflection groups