Multiplier ideals and klt singularities via (derived) splittings

2023/07/15 by McDonald, Peter M.
#13A35 #14B05 #14E15 #14F18 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.07906

Abstract

Let X be a normal, excellent, noetherian scheme over Specℚ with a dualizing complex. In this note, we find an alternate characterization of the multiplier ideal of X, as defined by de Fernex-Hacon, by considering maps π_*ω_Y\toO_X where π:Y→ X ranges over all regular alterations. As a corollary to this result, we give a derived splinter characterization of klt singularities, akin to the characterization of rational singularities given by Kovács and Bhatt. We also give an analogous description of the test ideal in characteristic p>2 as a corollary to a result of Epstein-Schwede.

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