The Picard group of Brauer-Severi varieties.

What is it about?

In this note, we show an explicit concrete generator of the Picard group of any Brauer-Severi variety corresponding to a cyclic algebra in its class inside the Brauer group Br(k) of k. In particular, for a Brauer-Severi surface B and any integer r ≥ 1, we obtain a generator for r Pic(B) from twists of a Fermat type smooth plane curve, see Theorem 4.2. Moreover, we can write equations in ℙ^9.

Featured Image