Generic bounds for Frobenius closure and tight closure
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...
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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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Let I denote an R+-primary homogeneous ideal in a normal standard-graded Cohen-Macaulay domain over a field of positive characteristic p. We give a linear degree bound for the Frobenius powers I [q] of I, q = p, in terms of the minimal slope of the top-dimensional syzygy bundle on the projective variety ProjR. This provides an inclusion bound for tight closure. In the same manner we give a line...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2011
ISSN: 1080-6377
DOI: 10.1353/ajm.2011.0032