Note on Bounds for Multiplicities
نویسنده
چکیده
Let S = K[x1, . . . , xn] be a polynomial ring and R = S/I be a graded K-algebra where I ⊂ S is a graded ideal. Herzog, Huneke and Srinivasan have conjectured that the multiplicity of R is bounded above by a function of the maximal shifts in the minimal graded free resolution of R over S. We prove the conjecture in the case that codim(R) = 2 which generalizes results in [10] and [13]. We also give a proof for the bound in the case in which I is componentwise linear. For example, stable and squarefree stable ideals belong to this class of ideals.
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