Upper Bounds for the Betti Numbers of a given Hilbert Function
نویسنده
چکیده
Let R := k[X1, . . . , XN ] be the polynomial ring in N indeterminates over a field k of characteristic 0 with deg(Xi) = 1 for i = 1, . . . , N , and let I be a homogeneous ideal of R . The Hilbert function of I is the function from N to N which associates to every natural number d the dimension of Id as a k -vectorspace. I has an essentially unique minimal graded free resolution 0 −→ Lm dm −→Lm−1 dm−1 −→ . . . d2 −→L1 d1 −→L0 d0 −→I −→ 0 which is characterized, among the free graded resolutions, by the condition dq(Lq) ⊆ (X1, . . . , XN)Lq−1 ∀ q ≥ 1
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