minimal free resolution

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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. AbstractWebsite

Let 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;

"On the Homogenous Ideal of General Points in P 5." International Journal of Algebra. 2016;10(6):265-282. AbstractWebsite

Given 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

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