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Arithmetical Rank of a Squarefree Monomial Ideal whose Alexander Dual is of Deviation Two

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Abstract

In this paper, we prove that the arithmetical rank of a squarefree monomial ideal I of a polynomial ring S is equal to the projective dimension of S/I when arithdeg I−indeg I=2 and I has a linear resolution.

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Acknowledgments

This work was partially supported by JSPS Grant-in-Aid for Scientific Research (C) 25400050/26400049 and JSPS Grant-in-Aid for Young Scientists (B) 24740008.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Shizuoka University, 836 Ohya, Suruga-ku, Shizuoka, 422-8529, Japan

    Kyouko Kimura

  2. Department of Mathematics, Faculty of Culture and Education, Saga University, Saga, 840-8502, Japan

    Naoki Terai

  3. Department of Mathematics, College of Humanities and Sciences, Nihon University, 3-25-40 Sakurajosui, Setagaya-ku, Tokyo, 156-8550, Japan

    Ken-ichi Yoshida

Authors
  1. Kyouko Kimura
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  2. Naoki Terai
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  3. Ken-ichi Yoshida
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Correspondence to Kyouko Kimura.

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Dedicated to Ngo Viet Trung on the occasion of his sixtieth birthday

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Kimura, K., Terai, N. & Yoshida, Ki. Arithmetical Rank of a Squarefree Monomial Ideal whose Alexander Dual is of Deviation Two. Acta Math Vietnam 40, 375–391 (2015). https://doi.org/10.1007/s40306-015-0136-x

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  • DOI: https://doi.org/10.1007/s40306-015-0136-x

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