Abstract
A set of points in the projective plane is said to be Cremona special if its orbit with respect to the Cremona group of birational transformations consists of finitely many orbits of the projective group. This notion was extended by A. Coble to sets of points in higher–dimensional projective spaces and by S. Mukai to sets of points in the product of projective spaces. No classification of such sets is known in these cases. In the present article we survey Coble’s examples of Cremona special points in projective spaces and initiate a search for new examples in the case of products of projective spaces. We also extend to the new setting the classical notion of associated points sets.
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