A variety is unirational if
there is a map
from an open subset
of some affine space whose image contains a dense,
open subset of . For instance,
is unirational means that
there is a family of curves on an open subset of affine space which
contains a general curve of genus . This is known to be the case
for . Moreover, since unirational implies Kodaira
dimension , the result of Eisenbud, Harris, and Mumford shows
that
is not unirational for .

Jeffrey Herschel Giansiracusa
2005-06-27