Curve selection for finite-type ideals

Details Curve selection for finite-type ideals Curve selection for finite-type ideals

2005-06-28

arxiv.org/abs/math/0506557v2

Mathematics

Complex Variables

This paper has become part of "Finite type and the effective Nullstellensatz" (math.AG/0603666)

Scientific paper

Let $\mathfrak a$ be an ideal of holomorphic functions vanishing only at the origin in $\mathbb{C}^n$. The \textit{type} of $\mathfrak a$ is an invariant that measures the order of vanishing of the functions in $\mathfrak a$ along holomorphic curves; this invariant is of importance in the study of subelliptic estimates and subelliptic multiplier ideal sheaves. Recently there has been some interest in the question of which curves actually compute the type. In this note we prove that it is computed by one of the analytic irreducible components of the intersection of $n-1$ general functions in $\mathfrak a$.

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