F-injective singularities are Du Bois

By Karl Schwede. 2008

80 citations recorded by the source corpus.

In this paper, we prove that singularities of $F$-injective type are Du~Bois. This extends the correspondence between singularities associated to the minimal model program and singularities defined by the action of Frobenius in positive characteristic.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aecc7f919e071e251c397d7bb85169ee45cf4f01

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Centers of F-purity (2008, background): “The statement about Du Bois singularities follows immediately from the fact that F-pure singularities are F-injective and from [ 34, Theorem 6.1 ].”
A canonical linear system associated to adjoint divisors in characteristic $p > 0$ (2011, background): “, MS97]. F-pure pairs are the analog of log canonical pairs in characteristic zero [HW02]. Finally, F-injective varieties are the analog of varieties with Du Bois singularities in characteristic zero [Sch09b]. 6 KARL SCHWEDE 3. Motivationalcomputationsandeasy cases Suppose that Xis a smooth (or simp”
A guide to closure operations in commutative algebra (2011, background): “re are connections to characteristic 0 singularity theory. Namely, if R is a reduced, ﬁnitely generated Q -algebra (or C -algebra) of dense F-injective type, then SpecR has only Du Bois singularities [Sch09]. (A converseis not known.) Example (Tight closure). By deﬁnition, a ring R of prime characte”
A survey of test ideals (2011, background): “ natural map Hi m(R) →Hi m(R 1/p) is injective for every i≥0 and every maximal ideal m⊆R. See [Fed83]. Finjective rings are closely related to rings with Du Bois singularities in characteristic zero, [Sch09b]. F-ideal: Suppose that (R,m) is a local ring. An ideal I⊆Ris called an F-ideal if MI := Ann”
Hodge theory meets the minimal model program: a survey of log canonical and Du Bois singularities (2009, methodology): “tive type if for every family of characteristic p ≫0 models with A chosen suﬃciently large, we have that a Zariski dense set of those models (over SpecA) have F-injective singularities. Theorem 13.7. [Sch09] Let X be a reduced scheme of ﬁnite type over C and assume that it has dense F-injective type”