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