English

Proper polyhedral divisors and torus actions over arbitrary fields

Algebraic Geometry 2025-10-01 v4

Abstract

We provide a algebro-geometric combinatorial description of geometrically integral geometrically normal affine varieties endowed with an effective action of an algebraic torus over arbitrary fields. This description is achieved in terms of proper polyhedral divisors endowed with a Galois semilinear action.

Keywords

Cite

@article{arxiv.2506.22734,
  title  = {Proper polyhedral divisors and torus actions over arbitrary fields},
  author = {Gary Martinez-Nunez},
  journal= {arXiv preprint arXiv:2506.22734},
  year   = {2025}
}

Comments

69 pages, comments are welcome :)There are some improvements in the redaction. Also, Proposition 4.5 has been corrected and Proposition 4.6 has been added. Improvement in the section of Galois descent

R2 v1 2026-07-01T03:37:32.542Z