Seminario / Nijgh
SEMINARIO DI GEOMETRIA ALGEBRICA
Nell'ambito del seminario congiunto di geometria algebrica
organizzato dai Dipartimenti di Matematica dell'Università e del Politecnico di Milano,
giovedì 15 Giugno alle 13:00 (durata 1 ora)
in Aula Dottorato del Dipartimento di Matematica "F. Enriques",
si terrà il seguente seminario: Abstract:
Wim Nijgh
(Universiteit Leiden)
On the Galois-invariant part of the Weyl group of the Picard lattice of a K3 surface
(j.w. R. v. Luijk)
Let X denote a K3 surface over an arbitrary field k. Let k^s denote a separable closure of k and let X^s denote the base change of X to k^s. Let O(Pic X) and O (Pic X^s) denote the group of isometries of the lattices Pic X and Pic X^s, respectively. Let R_X denote the Galois invariant part of the Weyl group of Pic X^s. 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.
13 giugno 2023