  We prove that the standard norm varieties for Milnor symbols mod p of length
n are birationally isomorphic to Pfister quadrics when p = 2, to Severi-Brauer
varieties when p > 2, n = 2, and to varieties defined by reduced norms of
cyclic algebras when p > 2, n = 3. In the case p = 2 and the case p > 2, n = 2,
the results imply that the standard norm varieties for two equal Milnor symbols
mod p are birationally isomorphic, and we conjecture this in general.
