Bound on the multiplicity of almost complete intersections
Abstract
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 $\prod_{i=1}^N d_i - \max\{1, \sum_{i=1}^N (d_i-1) - (d_{N+1}-1) \}$.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2008
- DOI:
- 10.48550/arXiv.0802.0469
- arXiv:
- arXiv:0802.0469
- Bibcode:
- 2008arXiv0802.0469E
- Keywords:
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- Mathematics - Commutative Algebra;
- 13B22;
- 13H15
- E-Print:
- 7 pages