Abstract
Two reduced projective schemes are said to be Cremona equivalent if there is a Cremona map that maps one in the other. In this paper I revise some of the known results about Cremona equivalence and extend the main result of Mella and Polastri (Bull Lond Math Soc 41(1):89–93, 2009) [20] to reducible schemes. This allows to prove a very general contractibility result for union of rational subvarieties.
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