For perfect fields k with algebraic closure L satisfying [L:k] > 2, we construct new normal subgroups of the plane Cremona group and provide an elementary proof of its non-simplicity, following the melody of the recent proof by Blanc, Lamy and Zimmermann that the Cremona group of rank n over (subfields of) the complex numbers is not simple for n ≥ 3.
Plane curves of fixed bidegree and their A_k-singularities
We provide a tool how one can view a polynomial on the affine plane of bidegree (a,b) - by which we mean that its Newton polygon lies in the triangle spanned by (a,0), (0,b) and the origin - as a curve in a Hirzebruch surface having nice geometric properties. As an application, we study maximal Ak-singularities of curves of bidegree (3,b) and find the answer for b ≤ 12.
Departement Mathematik und Informatik