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


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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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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Correspondence to 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).

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Mathematics Subject Classification

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