• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.545-550
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• 2005

We find a necessary and sufficient condition that the number of some Betti numbers and shifts appear in the last free module Fn of Fx based on type vectors, where X is a finite set of points in $P^n$.

• East Asian mathematical journal
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• v.36 no.3
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• pp.349-357
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• 2020

For a nondegenerate projective curve C ⊂ ℙ^r of degree d, it was shown that the Castelnuovo-Mumford regularity reg(C) of C is at most d - r + 2. And the curves of maximal regularity which attain the maximally possible value d - r + 2 are completely classified. In this short note, we first collect several known results about curves of maximal regularity. We provide a new proof and some partial results. Finally we suggest some interesting questions.