Bound on the multiplicity of almost complete intersections

Details Bound on the multiplicity of almost complete intersections Bound on the multiplicity of almost complete intersections

2008-02-04

arxiv.org/abs/0802.0469v1

Communications in Algebra 37 (2009), 948-953

Mathematics

Commutative Algebra

7 pages; to appear in Communications in Algebra

Scientific paper

10.1080/00927870802278784

Let $R$ be a polynomial ring over a field of characteristic zero and let $I \subset R$ be a graded ideal of height $N$ which is minimally generated by $N+1$ homogeneous polynomials. If $I=(f_1,...,f_{N+1})$ where $f_i$ has degree $d_i$ and $(f_1,...,f_N)$ has height $N$, then the multiplicity of $R/I$ is bounded above by $\prod_{i=1}^N d_i - \max\{1, \sum_{i=1}^N (d_i-1) - (d_{N+1}-1) \}$.

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