EQUATIONS OF SOME EMBEDDINGS OF A PROJECTIVE SPACE INTO ANOTHER ONE
Résumé
In [8], Eisenbud, Huneke and Ulrich conjectured a result on the Castelnuovo-Mumford regularity of the embedding of a projective space P n−1 ֒→ P r−1 determined by generators of a linearly presented m-primary ideal. This result implies in particular that the image is scheme defined by equations of degree at most n. In this text we prove that the ideal of maximal minors of the Jacobian dual matrix associated to the input ideal defines the image as a scheme; it is generated in degree n. Showing that this ideal has a linear resolution would imply that the conjecture in [8] holds. Furthermore, if this ideal of minors coincides with the one of the image in degree n-what we hope to be true-the linearity of the resolution of this ideal of maximal minors is equivalent to the conjecture in [8].
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