Tight closure and plus closure in dimension two
نویسندگان
چکیده
منابع مشابه
Tight Closure and plus Closure in Dimension Two
We prove that the tight closure and the graded plus closure of a homogeneous ideal coincide for a two-dimensional N-graded domain of finite type over the algebraic closure of a finite field. This answers in this case a “tantalizing question” of Hochster. Mathematical Subject Classification (2000): 13A35; 14H60
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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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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...
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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...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2006
ISSN: 1080-6377
DOI: 10.1353/ajm.2006.0011