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- W2072963913 abstract "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) and we predict the existence of a non-empty open subset U⊂Hilbs(X) such that any [Z]∈U has a minimal graded free resolution without ghost terms (WMRC). In this paper, we are going to prove: (1) for any s⩾(d+33)−1 there exists a (d+22)-dimensional family of irreducible generically smooth surfaces of degree d in P3 satisfying the WMRC for s; and (2) any smooth cubic surface satisfies the MRC for any s⩾19." @default.
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- W2072963913 date "2012-05-01" @default.
- W2072963913 modified "2023-09-30" @default.
- W2072963913 title "Minimal free resolution for points on surfaces" @default.
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- W2072963913 doi "https://doi.org/10.1016/j.jalgebra.2012.01.034" @default.
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