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“\({\mathbb {P}}^1\)-gluing” for local complete intersections

Mathematische Zeitschrift volume 294, pages 667–685 (2020)Cite this article

Abstract

We prove an analogue of the Affine Horrocks’ Theorem for local complete intersection ideals of height n in R[T], where R is a regular domain of dimension d, which is essentially of finite type over an infinite perfect field of characteristic unequal to 2, and \(2n\ge d+3\).

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Acknowledgements

We are grateful to the referee for an extremely meticulous reviewing and for pointing out a serious gap in one of our arguments. The clarity of exposition in the present version owes very much to the insistence of the referee. We sincerely thank Ravi Rao for answering numerous queries. We are deeply indebted to S. M. Bhatwadekar for his critical reading of an earlier version and for pointing out a mistake in the proof of Theorem 3.10. The question tackled in this article was proposed to the first named author by S. M. Bhatwadekar and Raja Sridharan around the year 2000, as a part of his thesis problem. The first named author takes this opportunity to thank them once again for their care and encouragement. The third named author acknowledges Department of Science and Technology for their INSPIRE research grant.

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Author notes

  1. Md. Ali Zinna

    Present address: Department of Mathematics and Statistics, Indian Institute of Science Education and Research Kolkata, Mohanpur, Nadia, 741246, West Bengal, India

Authors and Affiliations

  1. Stat-Math Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata, 700108, India

    Mrinal Kanti Das & Soumi Tikader

  2. School of Mathematical Sciences, National Institute of Science Education and Research Bhubaneswar (HBNI), Odisha, 752050, India

    Md. Ali Zinna

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  1. Mrinal Kanti Das
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Das, M.K., Tikader, S. & Zinna, M.A. “\({\mathbb {P}}^1\)-gluing” for local complete intersections. Math. Z. 294, 667–685 (2020). https://doi.org/10.1007/s00209-019-02299-5

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  • DOI: https://doi.org/10.1007/s00209-019-02299-5

Mathematics Subject Classification

  • 13C10
  • 19A15
  • 14C25
  • 11E81