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I had the impression that there were false claims concerning rationality of certain Fano varieties, but I don't have any specific references on hand. For a more definite example, take a look the introduction to Mumford's "Rational equivalence of 0-cycles on surfaces". In this paper, he disproves something that Severi took as self evident.

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I had the impression that there false claims concerning rationality of certain Fano varieties, but I don't have any specific references on hand. For a more definite example, take a look the introduction to Mumford's "Rational equivalence of 0-cycles on surfaces". In this paper, he disproves something that Severi took as self evident.