Seminormality and local cohomology of toric face rings

Autor(en): Dang Hop Nguyen
Stichwörter: ALGEBRAS; COHEN-MACAULAY RINGS; COMPLEXES; F-injectivity; F-purity; F-regularity; Local cohomology; Mathematics; Monoid rings; PARTIALLY ORDERED SETS; PURITY; Seminormality; Toric face rings
Erscheinungsdatum: 2012
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: JOURNAL OF ALGEBRA
Volumen: 371
Startseite: 536
Seitenende: 553
Zusammenfassung: 
We characterize the toric face rings that are normal (respectively seminormal). Extending results about local cohomology of Brun, Bruns, Ichim, Li and Romer of seminormal monoid rings and Stanley toric face rings, we prove the vanishing of certain graded parts of local cohomology of seminormal toric face rings. The combinatorial formula we obtain generalizes Hochster's formula. We also characterize all (necessarily seminormal) toric face rings that are F-pure or F-split over a field of characteristic p > 0. An example is given to show that F-injectivity does not behave well with respect to face projections of toric face rings. Finally, it is shown that weakly F-regular toric face rings are normal affine monoid rings. (C) 2012 Elsevier Inc. All rights reserved.
ISSN: 00218693
DOI: 10.1016/j.jalgebra.2012.08.017

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