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Acta Mathematica Vietnamica

, Volume 40, Issue 3, pp 535–544 | Cite as

On the Relation Type of Fiber Cone

  • A. V. Jayanthan
  • Ramakrishna Nanduri
Article
  • 114 Downloads

Abstract

In this article, we study the relation type of the fiber cone of certain special classes of ideals in Noetherian local rings. We show that in any Noetherian local ring, if deviation of I is 1, and depth\((G(\mathcal F_{L})) \geq \ell -1\), then the relation types of \(\mathcal {R}(I)\) and F L (I) are equal. We also prove that for lexsegment ideals in K[x,y], where K is a field, the relation types of the fiber cone and the Rees algebra are equal.

Keywords

Relation type Fiber cone Rees algebra Associated graded ring Lexsegment ideal Equimultiple ideal Deviation 

Mathematics Subject Classification (2010)

Primary 13A30 Secondary 13A02 

Notes

Acknowledgments

The authors are grateful to Professor A. Conca and Professor M. E. Rossi for some useful discussions on the content of this article. The authors are also thankful to Professor F. Planas-Vilanova for some discussions on the proof of Theorem 3.1. Part of this work was done when the second author was visiting University of Genova supported by INdAM-COFUND Marie Curie Fellowship, Italy. He is thankful to the Department of Mathematics, University of Genova, for the hospitality. They also wishes to express their sincere gratitude to the referee who went through the article carefully and pointed out some errors in the proofs of the initial draft.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia
  2. 2.Department of MathematicsIndian Institute of Technology KharagpurKharagpurIndia

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