Rational singularities associated to pairs

Details Rational singularities associated to pairs Rational singularities associated to pairs

2007-08-15

arxiv.org/abs/0708.1990v4

Michigan Math. J. 57 (2008), 625--658

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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