Papers › On the Galois-invariant part of the Weyl group of the Picard lattice of a K3 surface
On the Galois-invariant part of the Weyl group of the Picard lattice of a K3 surface
Wim Nijgh, Ronald van Luijk
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 X denote a K3 surface over an arbitrary field k. Let kˢ denote a separable closure of k and let Xˢ denote the base change of X to kˢ. The action of the absolute Galois group Gal(kˢ/k) of k on Pic Xˢ respects the intersection pairing, which gives Pic Xˢ the structure of a lattice. Let O(Pic X) and O(Pic Xˢ) denote the group of isometries of Pic X and Pic Xˢ, respectively. Let R_X denote the Galois invariant part of the Weyl group of O(Pic Xˢ). One can show that each element in R_X can be restricted to an element of O(Pic X). The following question arises: Is the image of the restriction map R_X →O(Pic X) a normal subgroup of O(Pic X) for every K3 surface X? We show that the answer is negative by giving counterexamples over k=ℚ.
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