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<p>We give a sufficient condition on a positive integer <i>m</i> for every stratum of a given real toric hyperplane arrangement to contain a rational point of denominator <i>m</i>. As a consequence, we give a sufficient condition on <i>m</i> for the degree <i>m</i> Frobenius pushforward of the structure sheaf on a smooth toric variety to contain all possible summands in the Picard group.</p>

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Rational points of fixed denominator in real toric arrangements

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月4日

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  • Andrew Hanlon,
  • Davis Painter

摘要

We give a sufficient condition on a positive integer m for every stratum of a given real toric hyperplane arrangement to contain a rational point of denominator m. As a consequence, we give a sufficient condition on m for the degree m Frobenius pushforward of the structure sheaf on a smooth toric variety to contain all possible summands in the Picard group.