On the rate of points in projective spaces |
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Authors: | Aldo Conca Emanuela De Negri Maria Evelina Rossi |
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Institution: | (1) Dipartimento di Matematica, Universitá di Genova, Via Dodecaneso 35, I-16146 Genova, Italy |
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Abstract: | The rate of a standard gradedK-algebraR is a measure of the growth of the shifts in a minimal free resolution ofK as anR-module. It is known that rate(R)=1 if and only ifR is Koszul and that rate(R) ≥m(I)−1 wherem(I) denotes the highest degree of a generator of the defining idealI ofR. We show that the rate of the coordinate ring of certain sets of pointsX of the projective space P
n
is equal tom(I)−1. This extends a theorem of Kempf. We study also the rate of algebras defined by a space of forms of some fixed degreed and of small codimension. |
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