English

Rational points of fixed denominator in real toric arrangements

Combinatorics 2026-02-16 v2 Algebraic Geometry

Abstract

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

Keywords

Cite

@article{arxiv.2408.07164,
  title  = {Rational points of fixed denominator in real toric arrangements},
  author = {Andrew Hanlon and Davis Painter},
  journal= {arXiv preprint arXiv:2408.07164},
  year   = {2026}
}

Comments

8 pages, 2 figures, v2:minor updates in exposition