## : maximal rank

Ben Obiero, Maingi D. "

On the Minimal Resolution Conjecture for the Ideal of General Points in P 4."

*Pure Mathematical Sciences*. 2017;6(1):, 67-85.

AbstractLet X={P1,..., Ps}⊆ Pn, with s≥ n+ 1, be a set of points in general position, and S be the sub-scheme supported at these points. The minimal resolution conjecture asserts that the homogeneous ideal of this sub-scheme, IS⊂ R= k [x0,..., xn], where k is an algebraically closed field and R the homogeneous coordinate ring of Pn, has the following expected form;

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On the Homogenous Ideal of General Points in P 5."

*International Journal of Algebra*. 2016;10(6):265-282.

AbstractGiven a set of s points in Pn, the Hilbert Syzygy theorem asserts that the ideal defined by these points has a resolution of the form 0−→ Fp−→···−→ F0−→ IX−→ 0 where p≤ n− 1. If the points under consideration are in general position, then the minimal resolution conjecture gives the