The Noether problem for spinor groups of small rank

Abstract

Building on prior work of Bogomolov, Garibaldi, Guralnick, Igusa, Kordonskii, Merkurjev and others, we show that the Noether Problem for ${\mathrm{Spin}}_n$ has a positive solution for every $n\le 14$ over an arbitrary field of characteristic $\ne 2$.

Added an alternative proof of Theorem 1.1 over the complex numbers, suggested by G. Schwarz