Abstract
A rational map whose source and image are projectively embedded varieties is said to have an arithmetically Cohen–Macaulay graph if the Rees algebra of one (hence any) of its base ideals is a Cohen–Macaulay ring. The main objective of this paper is to obtain an upper bound for the degree of a representative of the map in case it is birational onto the image with an arithmetically Cohen–Macaulay graph. In the plane case a complete classification is given of the Cremona maps with arithmetically Cohen–Macaulay graph, while in arbitrary dimension n it is shown that a Cremona map with arithmetically Cohen–Macaulay graph has degree at most n2.
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