Rational singularities associated to pairs

Abstract

In this paper we introduce a notion of rational singularities associated to pairs $(X, \ba^t)$ where $X$ is a variety, $\ba$ is an ideal sheaf and $t$ is a nonnegative real number. We prove that most standard results about rational singularities extend to this context. We also show that some results commonly associated with log terminal pairs have analogs in this context, including results related to inversion of adjunction. A positive characteristic analogue of rational singularities of pairs is also defined and explored.

31 pages; v.4: a minor mistake in the characteristic p theory is corrected, see Remark 1.1 for details

References in corpus (2)

• F-thresholds and Bernstein-Sato polynomials
• On the discreteness and rationality of F-jumping coefficients

Cited by in corpus (1)

• Jumping Numbers on Algebraic Surfaces with Rational Singularities