Papers › Linear system of hypersurfaces passing through a Galois orbit
Linear system of hypersurfaces passing through a Galois orbit
Shamil Asgarli, Dragos Ghioca, Zinovy Reichstein
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Let d and n be positive integers, and E/F be a separable field extension of degree m=n+dn. We show that if |F| > 2, then there exists a point P∈ℙⁿ(E) which does not lie on any degree d hypersurface defined over F. In other words, the m Galois conjugates of P impose independent conditions on the m-dimensional F-vector space of degree d forms in x₀, x₁, …, xₙ. As an application, we determine the maximal dimensions of linear systems ℒ₁ and ℒ₂ of hypersurfaces in ℙⁿ over a finite field F, where every F-member of ℒ₁ is reducible and every F-member of ℒ₂ is irreducible.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections