On Birational Maps and Jacobian Matrices
Francesco Russo,Aron Simis +1 more
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TLDR
In this article, a criterion for birationality in terms of certain syzygies and ranks of appropriate matrices is proposed and a method to explicitly obtain the inverse map is given.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.read more
Citations
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References
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Arithmetic of Blowup Algebras
TL;DR: In this paper, the authors provide an introduction to recent developments in the theory of blow up algebras - Rees algesbras, associated graded rings, Hilbert functions, and birational morphisms.