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On the Relation Type of Fiber Cone

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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.

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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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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600036, India

    A. V. Jayanthan

  2. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, 721302, India

    Ramakrishna Nanduri

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  1. A. V. Jayanthan
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  2. Ramakrishna Nanduri
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Correspondence to A. V. Jayanthan.

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Dedicated to Professor Ngô Việt Trung on the occasion of his 60th birthday

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Jayanthan, A.V., Nanduri, R. On the Relation Type of Fiber Cone. Acta Math Vietnam 40, 535–544 (2015). https://doi.org/10.1007/s40306-015-0142-z

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