Abstract
One is concerned with Cremona-like transformations, i.e., rational maps from ℙn to ℙm that are birational onto the image Y ⊂ ℙm and, moreover, the inverse map from Y to ℙn lifts to ℙm. We establish a handy criterion of birationality in terms of certain syzygies and ranks of appropriate matrices and, moreover, give an effective method to explicitly obtaining the inverse map. A handful of classes of Cremona and Cremona-like transformations follow as applications.
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Russo, F., Simis, A. On Birational Maps and Jacobian Matrices. Compositio Mathematica 126, 335–358 (2001). https://doi.org/10.1023/A:1017572213947
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DOI: https://doi.org/10.1023/A:1017572213947