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 ${\prod }_{i=1}^N{d}_i-\max \{1,{\sum }_{i=1}^N(d_i-1)-(d_{N+1}-1)\}$.

7 pages; to appear in Communications in Algebra

References in corpus (2)

• A formula for the core of an ideal
• On the projective dimension and the unmixed part of three cubics

Cited by in corpus (1)

• A Cayley-Bacharach theorem for points in ${\mathbb{P}}^n$