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<p>We prove that the Gorensteinification of the face ring of a cycle is totally <i>p</i>-anisotropic in characteristic <i>p</i>. In other words, given an appropriate Artinian reduction, it contains no nonzero <i>p</i>-isotropic elements. Moreover, we prove that the linear system of parameters can be chosen corresponding to a geometric realization with points on the moment curve. In particular, this implies that the parameters do not have to be chosen very generically.</p>

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p-Anisotropy on the Moment Curve for Homology Manifolds and Cycles

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • Karim Alexander Adiprasito,
  • Kaiying Hou,
  • Daishi Kiyohara,
  • Daniel Koizumi,
  • Monroe Stephenson

摘要

We prove that the Gorensteinification of the face ring of a cycle is totally p-anisotropic in characteristic p. In other words, given an appropriate Artinian reduction, it contains no nonzero p-isotropic elements. Moreover, we prove that the linear system of parameters can be chosen corresponding to a geometric realization with points on the moment curve. In particular, this implies that the parameters do not have to be chosen very generically.