Multiplier ideals and klt singularities via (derived) splittings

Author:

Peter M. McDonald

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Commutative Algebra (math.AC)

journal:

date:

2023-07-14 16:00:00

Abstract

In this note we find an alternate characterization of the multiplier ideal of a normal variety $X$, as defined by de Fernex-Hacon, by considering maps $\pi_*\omega_Y\to\mathcal{O}_X$ where $\pi:Y\to X$ 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 Kov\'acs 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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