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On Burch's inequality and a reduction system of a filtration |
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| Authors: | Y. Kinoshita K. Nishida Y. Yamanaka A. Yoneda |
| Affiliation: | Division of Mathematical Sciences and Physics, School of Science and Technology, Chiba University, 263-8522, Japan K. Nishida ; Division of Mathematical Sciences and Physics, School of Science and Technology, Chiba University, 263-8522, Japan ; Division of Mathematical Sciences and Physics, School of Science and Technology, Chiba University, 263-8522, Japan A. Yoneda ; Division of Mathematical Sciences and Physics, School of Science and Technology, Chiba University, 263-8522, Japan |
| Abstract: | Let  be a multiplicative filtration of a local ring such that the Rees algebra  is Noetherian. We recall Burch's inequality for  and give an upper bound of the a-invariant of the associated graded ring  using a reduction system of  . Applying those results, we study the symbolic Rees algebra of certain ideals of dimension  . |
| Keywords: | Multiplicative filtration Rees algebra associated graded ring |
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