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Test ideals in diagonal hypersurface rings, II

✍ Scribed by Moira A. McDermott

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
96 KB
Volume
264
Category
Article
ISSN
0021-8693

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✦ Synopsis

where k is a field of characteristic p, p does not divide d and n 3. We describe a method for computing the test ideal for these diagonal hypersurface rings. This method involves using a characterization of test ideals in Gorenstein rings as well as developing a way to compute tight closures of certain ideals despite the lack of a general algorithm. In addition, we compute examples of test ideals in diagonal hypersurface rings of small characteristic (relative to d) including several that are not integrally closed. These examples provide a negative answer to Smith's question [K.E. Smith, The multiplier ideal is universal test ideal, Comm. Algebra 28 (12)

πŸ“œ SIMILAR VOLUMES

Test Ideals in Diagonal Hypersurface Rin
Test Ideals in Diagonal Hypersurface Rings
✍ Moira A McDermott πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 86 KB

Let R s k x , . . . , x r x q ΠΈΠΈΠΈ qx , where k is a field of characteristic p, p does not divide d, and n G 3. If pd, then the test ideal for R is contained in Ε½ . py 1 Ε½ . py 1 x , . . . , x . If d s p q 1, then the test ideal for R is equal to x , . . . , x .