The rate of a standard graded K-algebra R is a measure of the growth of the shifts in a minimal free resolution of K as an R-module. It is known that rate(R) = 1 if and only if R is Koszul and that rate(R) >= m(I) - 1 where m(I) denotes the highest degree of a generator of the defining ideal I of R. We show that the rate of the coordinate ring of certain sets of points X of the projective space P^n is equal to m(I) - 1. This extends a theorem of Kempf. We study also the rate of algebras defined by a space of forms of some fixed degree d and of small codimension.
On the rate of points in projective spaces
CONCA, ALDO;DE NEGRI, EMANUELA;ROSSI, MARIA EVELINA
2001-01-01
Abstract
The rate of a standard graded K-algebra R is a measure of the growth of the shifts in a minimal free resolution of K as an R-module. It is known that rate(R) = 1 if and only if R is Koszul and that rate(R) >= m(I) - 1 where m(I) denotes the highest degree of a generator of the defining ideal I of R. We show that the rate of the coordinate ring of certain sets of points X of the projective space P^n is equal to m(I) - 1. This extends a theorem of Kempf. We study also the rate of algebras defined by a space of forms of some fixed degree d and of small codimension.
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