Abstract
We are interested in the smallest number s = s(n, q) such that, for any given n distinct F-q-rational points P-1, . . . , P-n is an element of Pn-1, there exists a hypersurface H of degree s and defined over F-q such that P-1, . . . , Pn-1 is an element of H, P-n is not an element of H. Alternately, s(n, q) is the maximal Castelnuovo-Mumford regularity of a set of n F-q-rational points in some ...
Abstract
We are interested in the smallest number s = s(n, q) such that, for any given n distinct F-q-rational points P-1, . . . , P-n is an element of Pn-1, there exists a hypersurface H of degree s and defined over F-q such that P-1, . . . , Pn-1 is an element of H, P-n is not an element of H. Alternately, s(n, q) is the maximal Castelnuovo-Mumford regularity of a set of n F-q-rational points in some projective space. Finally, s(n, q) is the index of stability of certain one-dimensional local Cohen-Macaulay rings.
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