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A long-standing problem in Algebraic Geometry and Commutative Algebra is to determine the minimal graded free resolution of a 0-dimensional scheme Z in Pn or in an arbitrary projective variety X. In [18], M. Mustaţă (1998) predicted the graded Betti numbers of the minimal free resolution of a general set of distinct points Z in X. In this paper, we state a refined version of Mustaţăʼs conjecture (MRC)...
Let R=k[x1,…,xn] be a polynomial ring and let I⊂R be a graded ideal. In [T. Römer, Betti numbers and shifts in minimal graded free resolutions, arXiv: AC/070119], Römer asked whether under the Cohen–Macaulay assumption the ith Betti number βi(R/I) can be bounded above by a function of the maximal shifts in the minimal graded free R-resolution of R/I as well as bounded below by a function of the minimal...
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