Comparing multiplier ideals to test ideals on numerically Q-Gorenstein varieties

Abstract

We show that the reduction to positive characteristic of the multiplier ideal in the sense of de Fernex and Hacon agrees with the test ideal for infinitely many primes, assuming that the variety is numerically Q-Gorenstein. It follows, in particular, that this reduction property holds in dimension 2 for all normal surfaces.

11 pages; v2: minor changes, to appear in Bull. London Math. Soc

Cited by in corpus (2)

• Test ideals in rings with finitely generated anti-canonical algebras
• The jumping coefficients of non-Q-Gorenstein multiplier ideals