GENERIC BOUNDS FOR FROBENIUS CLOSURE AND TIGHT CLOSURE

Autor(en): Brenner, Holger 
Fischbacher-Weitz, Helena
Stichwörter: ALGEBRAS; Mathematics
Erscheinungsdatum: 2011
Herausgeber: JOHNS HOPKINS UNIV PRESS
Journal: AMERICAN JOURNAL OF MATHEMATICS
Volumen: 133
Ausgabe: 4
Startseite: 889
Seitenende: 912
Zusammenfassung: 
We use geometric and cohomological methods to show that given a degree bound for membership in ideals of a fixed degree type in the polynomial ring P = k[x(0), ... , x(d)], one obtains a good generic degree bound for membership in the tight closure of an ideal of that degree type in any standard-graded k-algebra R of dimension d 1. This indicates that the tight closure of an ideal behaves more uniformly than the ideal itself. Moreover, if R is normal, one obtains a generic bound for membership in the Frobenius closure. If d <= 2, then the bound for ideal membership in P can be computed from the known cases of the Froberg conjecture and yields explicit generic tight closure bounds.
ISSN: 00029327
DOI: 10.1353/ajm.2011.0032

Show full item record

Page view(s)

2
Last Week
0
Last month
0
checked on Feb 26, 2024

Google ScholarTM

Check

Altmetric