F-Thresholds, tight closure, integral closure, and multiplicity bounds
نویسندگان
چکیده
منابع مشابه
Generic Bounds for Frobenius Closure and Tight Closure
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[x1, . . . , xd], 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. This indicates that the tight closure of an ideal behaves more unif...
متن کاملSpecialization and integral closure
I ′/(x) = I ′/(x) , where x = ∑n i=1 ziai is a generic element for I defined over the polynomial ring R ′ = R[z1, . . . , zn] and I ′ denotes the extension of I to R. This result can be paraphrased by saying that an element is integral over I if it is integral modulo a generic element of the ideal. Other, essentially unrelated, results about lifting integral dependence have been proved by Teiss...
متن کاملTight Closure and Differential Simplicity
The behavior of the Hasse–Schmidt algebra under étale extension is used to show that the Hasse–Schmidt algebra of a smooth algebra of finite type over a field equals the ring of differential operators. These techniques show that the formation of Hasse–Schmidt derivations does not commute with localization, providing a counterexample to a question of Brown and Kuan; their conjecture is reformula...
متن کاملTight Closure and Projective Bundles
We formulate problems of tight closure theory in terms of projective bundles and subbundles. This provides a geometric interpretation of such problems and allows us to apply intersection theory to them. This yields new results concerning the tight closure of a primary ideal in a two-dimensional graded domain.
متن کاملTight Closure and plus Closure for Cones over Elliptic Curves
We characterize the tight closure of graded primary ideals in a homogeneous coordinate ring over an elliptic curve by numerical conditions and we show that it is in positive characteristic the same as the plus closure.
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2008
ISSN: 0026-2285
DOI: 10.1307/mmj/1220879419