In 1934 Severi claimed that the space of rational equivalence classes of cycles on an algebraic surface is finite - dimensional .
Mumford ( 1968 ) showed that this is false for surfaces of positive geometric genus .
In 1934 Severi claimed that the space of rational equivalence classes of cycles on an algebraic surface is finite - dimensional , but Mumford ( 1968 ) showed that this is false for surfaces of positive geometric genus .