# Unirational

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